Hyperidentities and related concepts. II. (English) Zbl 1404.08002
Summary: This survey article illustrates many important current trends and perspectives for the field including classification of hyperidentities, characterizations of algebras with hyperidentities, functional representations of free algebras, structure results for bilattices, categorical questions and applications. However, the paper contains new results and open problems, too.
For Part I, see [the author, ibid. 9, No. 2, 146–222 (2017; Zbl 1404.08001)].
For Part I, see [the author, ibid. 9, No. 2, 146–222 (2017; Zbl 1404.08001)].
MSC:
| 08A02 | Relational systems, laws of composition |
| 08A05 | Structure theory of algebraic structures |
| 08A40 | Operations and polynomials in algebraic structures, primal algebras |
| 08A62 | Finitary algebras |
| 06D30 | De Morgan algebras, Łukasiewicz algebras (lattice-theoretic aspects) |
| 06E05 | Structure theory of Boolean algebras |
| 20M07 | Varieties and pseudovarieties of semigroups |
| 20N05 | Loops, quasigroups |
Keywords:
hyperidentity; hypervariety; variety; termal hyperidentity; essential hyperidentity; bilattice; De Morgan algebra; Boole-De Morgan algebra; De Morgan function; quasi-De Morgan function; super-Boolean function; super-Boolean algebra; super-De Morgan algebra; super-De Morgan function; free algebraCitations:
Zbl 1404.08001Software:
JBoolReferences:
| [1] | L. R. Abrahamyan, Hyperidentities of ternary associativity. Proceedings of the Yerevan State University, Physical and Mathematical Sciences, 3(2003), pp. 36-44. |
| [2] | J. Acz´el,Forlesungen ¨uber Functionalgleichungen und ihre Anwendungem, Berlin, VEB Deutsch. Verl. Wiss., 1961. · Zbl 0096.09102 |
| [3] | J. Acz´el, Quelque probl“emes non-r´esolus dans la th´eorie des ´equations fonctionelles, in “Neki Nereˇseni Problemi u Matematici”, Beograd, 1963, pp. 149-152. · Zbl 0126.32002 |
| [4] | J. Acz´el, Proof of a theorem of distributive type hyperidentities. Algebra Universalis 1(1971), pp. 1-6. · Zbl 0219.08008 |
| [5] | J. Acz´el, J. Dhombres, Functional equations in several variables with applications to mathematics, information theory and to the natural and social sciences, Cambridge University Press, Cambridge, 1991. |
| [6] | M. Aguiar, M. Livernet, The associative operad and the weak order on the symmetric groups. J. Homotopy Relat. Struct., 2(2007), pp. 57-84. · Zbl 1184.18007 |
| [7] | A. A. Albert, Quasigroup I. Trans. Amer. Math. Soc. 54(1943), pp. 507-519. · Zbl 0063.00039 |
| [8] | A. A. Albert, Quasigroup II. Trans. Amer. Math. Soc. 55(1944), pp. 401-419. · Zbl 0063.00042 |
| [9] | A. D. Anosov, On homomorphisms of many-sorted algebraic systems in connection with cryptographic applications. Discrete Math. Appl. 17(4)(2007), pp. 331-347. · Zbl 1282.08005 |
| [10] | B. H. Arnold, Distributive lattices with a third operation defined. Pacific J. Math. 1(1951), pp. 33-41. · Zbl 0043.26501 |
| [11] | V. A. Artamonov, V. N. Salii, L. A. Skornyakov, L. N. Shevrin, E. G. Shulgeifer, General Algebra, Vol.2. Nauka, Moscow, 1991. (in Russian) · Zbl 0768.00004 |
| [12] | A. Avron, The structure of interlaced bilattices. Math. Struct. in Comp. Science 6(1996), pp. 287-299. · Zbl 0856.06005 |
| [13] | R. Balbes, Ph. Dwinger, Distributive Lattices, University of Missouri Press, 1974. · Zbl 0321.06012 |
| [14] | W. E. Barnes, On Γ-rings of Nobusawa. Pacific J. Math. 3(1966), pp. 411-422. · Zbl 0161.03303 |
| [15] | N. D. Belnap, A useful for valued logic. in: G. Epstein, J.M. Dunn (Eds)., Modern Uses of Multiple-Valued Logic, Reidel Publishing Comnpany, Boston, (1977), pp. 7-77. · Zbl 0424.03012 |
| [16] | N. D. Belnap, How computer should think. in: G. Ryle (Ed.), Contemporary Aspects of Philosophy, Oriel Press, (1977), pp. 30-56. |
| [17] | V. D. Belousov, The structure of distributive quasigroups. Mat. Sb. (N.S.) 50(92)(3)(1960), pp. 267-298. · Zbl 0097.01002 |
| [18] | V. D. Belousov, Systems of quasigroups with generalized identities. Russian Math. Surveys, 20(1965), pp. 73-143. · Zbl 0135.03503 |
| [19] | V. D. Belousov, Gratzer algebra and S-systems of quasigroups. Mat.Issled. Akad. Nauk. Mold. 1(1966), pp. 55-81. · Zbl 0229.08011 |
| [20] | V. D. Belousov, Foundations of the theory of quasigroups and loops, Nauka, Moscow, 1967. (in Russian) |
| [21] | V. D. Belousov, Yu. M. Movsisyan, On the rank of generalized identities, Izv. Akad. Nauk. Arm., ser. Mat. 9(1974), pp. 135-142. · Zbl 0308.20052 |
| [22] | G. B. Belyavskaya, A. M. Cheban, S-systems of arbitrary index I. Mat.Issled. Akad. Nauk. Mold. 7(1(23))(1972), pp. 23-43. · Zbl 0244.20097 |
| [23] | G. B. Belyavskaya, A. M. Cheban, S-systems of arbitrary index II. Mat.Issled. Akad. Nauk. Mold. 7(2(24))(1972), pp. 3-13. · Zbl 0282.20062 |
| [24] | G. M. Bergman, Hyperidentities of groups and semigroups. Aequationes Math., 23(1981), pp. 50-65. · Zbl 0453.08003 |
| [25] | G. M. Bergman, An invitation on general algebra and universal constructions, Second edition, Springer, 2015. · Zbl 1317.08001 |
| [26] | J. Berman, Distributive latticec with an additional operation. Aequationes Math. 16(1977), pp. 165-171. · Zbl 0395.06007 |
| [27] | J. Berman, A proof of Lyndon’s finite basis theorem. Discrete Math., 52(1980), pp. 229-233. · Zbl 0449.08004 |
| [28] | A. Bialynicki-Birula, H. Rasiowa, On the representation of quasiBoolean algebras. Bull. Acad. Polon. Sci., Ser. Math. Astronom. Phys. 5(1957), pp. 259-261. · Zbl 0082.01403 |
| [29] | G. Birkhoff, On the structure of abstract algebras. Proc. Cambridge Phil. Soc. 31(1953), pp. 433-454. · Zbl 0013.00105 |
| [30] | G. Birkhoff, Lattice Theory. 3rd edn., American Mathematical Society, Providence, Rhode Island, 1979. · Zbl 0505.06001 |
| [31] | G. Birkhoff, J. D. Lipson, Heterogeneous algebras. J. Combinat. Theory 8(1970), pp. 115-133. · Zbl 0211.02003 |
| [32] | W. J. Blok, The lattice of modal logics, an algebraic investigation. J. Symbolic Logic 45(1980), pp. 221-236. · Zbl 0436.03010 |
| [33] | S. L. Bloom, Z.Esik, E. G. Manes, A Cayley theorem for Boolean´ algebras. Amer. Math. Monthly 97(1990), pp. 831-833. · Zbl 0749.08002 |
| [34] | F. Bou, R. Jansana, U. Rivieccio, Varieties of interlaced bilattices. Algebra Universalis 66(2011), pp. 115-141. · Zbl 1231.06009 |
| [35] | S. J. Boyd, M. Gould, Interassociativity and isomorphism. Pure Math. Appl. 10(1) (1999), pp. 23-30. · Zbl 0938.20042 |
| [36] | S. J. Boyd, M. Gould, A. W. Nelson, Interassociativity of semigroups. Proceedings of the Tennessee Topology Conference, Nashville, TN, USA, 1996. Singapore: World Scientific, (1997), pp. 33-51. · Zbl 0915.20030 |
| [37] | R. H. Bruck, Contributions to the theory of loops. Trans. Amer. Math. Soc. 60(1946), pp. 245-354. · Zbl 0061.02201 |
| [38] | R. H. Bruck,A survey of binary systems. Berlin, Heidelberg, G¨ottingen, Springer, 1971. · Zbl 0206.30301 |
| [39] | J. A. Brzozowski, De Morgan bisemilattices. in: The 30th IEEE International Sympozium on Multiple-Valued Logic (Portland, Oregon, May 2000), IEEE Press, Los Alamitos, California, (2000), pp. 23-25. |
| [40] | J. A. Brzozowski, A characterization of De Morgan algebras. Int. J. Algebra Comput. 11(5)(2001), pp. 525-537. · Zbl 1025.06007 |
| [41] | J. A. Brzozowski, C.-J. H. Seger, Asynchronous Circuits, Springer Verlag, 1995. · Zbl 0747.94024 |
| [42] | S. Burris, H. P. Sankappanavar,A course in universal algebra, Springer-Verlag, 1981. · Zbl 0478.08001 |
| [43] | C. C. Chang, H. J. Keisler, Model Theory, Nort-Holland, Amsterdam, 1973. · Zbl 0276.02032 |
| [44] | O. Chein, H. O. Pflugfelder, J. D. H. Smith, Quasigroups and Loops: Theory and Applications, Sigma Series in Pure Math. 9, Heldermann Verlag, 1990. · Zbl 0704.00017 |
| [45] | G. Chupona, Za finitarnite operazii. Godishen zbornik univerzitetot Skopje, Prirodno-Matematichki Fakultet 1(12)(1959-1961), pp. 7-49. |
| [46] | A. Church, Introduction to mathematical logic, Vol. 1. Princeton University Press, Princeton, NJ 1956. · Zbl 0073.24301 |
| [47] | P. M. Cohn, Universal Algebra, Harper & Row Publishers, New York, Evanston and London, 1965. · Zbl 0141.01002 |
| [48] | D. Cowan, S. L. Wismath, Unari hyperidentities for varieties of inverse semigroups, Preprint, 1996. · Zbl 0919.20037 |
| [49] | Y. Crama, P. L. Hammer, Boolean Functions: Theory, Algorithms, and Applications, Cambridge University Press, 2011, New York. · Zbl 1237.06001 |
| [50] | S. S. Davidov, On invertible T -algebras. J. Math. Sci. (N.Y.) 193:3(2013), pp. 394-400. · Zbl 1292.20071 |
| [51] | S. S. Davidov, A characterization of binary invertible algebras linear over a group. Quasigroups and Related Systems 19(2011), pp. 207-222. · Zbl 1254.20060 |
| [52] | S. S. Davidov, A characterization of binary invertible algebras of various type of linearity. Quasigroups and Related Systems 20, (2012), pp. 169-176. · Zbl 1273.20071 |
| [53] | S. S. Davidov, On regular medial division algebras. Quasigroups and Related Systems 21(2013), pp. 157-166. · Zbl 1302.20070 |
| [54] | S. S. Davidov, A characterization of invertible algebras linear over a group by second-order formulas. J. Algebra Appl. 2017. DOI:10.1142/S0219498817502383. · Zbl 1415.20014 |
| [55] | S. S. Davidov, A. Krape˘z, Yu. M. Movsisyan, Functional Equations with Division and regular Operations. Asian-Eur. J. Math., 2(2018). |
| [56] | R. Dedekind, ¨Uber Zerlegungen von Zahlen durch ihre gr¨oßten gemeinsamen Teiler, Festschrift der Techn. Hochsch. Braunschwig bei Gelegenheit der 69(1897). Versammlung deutscher Naturforscher und Arzte, 1-40.¨ · JFM 28.0186.04 |
| [57] | K. Denecke, Hyperequational theory, Math. Japonica 47(1998), pp. 333-356. · Zbl 0909.20043 |
| [58] | K. Denecke, J. Koppitz, Presolid varieties of commutative semigroups. Tatra Mt. Math. Publ. 5(1995), pp. 41-48. · Zbl 0852.20047 |
| [59] | K. Denecke, J. Koppitz, Hyperassociative Varieties of Semigroups. Semigroup Forum 49(1994), pp. 41-48. · Zbl 0806.20049 |
| [60] | K. Denecke, D. Lau, R. P¨oschel, D. Schweigert, Hyperidentities, hyperequational classes, and clone congruences. Contribution to General Algebra 7, Verlag H¨older-Pichler-Tempsky, Wien, (1991), pp. 97-118. · Zbl 0759.08005 |
| [61] | K. Denecke, R. P¨oschel, A characterization of Sheffer functions by hyperidentities. Semigroup Forum 37(1988), pp. 351-362. · Zbl 0642.08002 |
| [62] | K. Denecke, R. P¨oschel, The characterization of primal algebras by hyperidentities. Contributions to General Algebra 6, Wien, (1988), pp. 67-87. · Zbl 0695.08007 |
| [63] | K. Denecke, S. L. Wismath, Hyperidentities and Clones. Gordon and Breach Science Publishers, 2000. · Zbl 0960.08001 |
| [64] | J. Denes, A. D. Keedwell,Lattin squares and their applications, Akademiai Kiado, Budapest, 1974 (also Academic Press, New York,1974, and English Universities Press, London, 1974). · Zbl 0283.05014 |
| [65] | L. E. Dickson, Definition of a group and a field by independent postulates. Trans. Amer. Math. Soc., 6(1905), pp. 198-204. · JFM 36.0207.01 |
| [66] | M. Drouzy, La structuration des ensembles de semigroupes dordre 2, 3 et 4 par la relation dinterassociativite. Manuscript (1986) |
| [67] | A. Ehsani, A. Krapez, Yu. M. Movsisyan, Algebras with Parastropically Uncancellable Quasigroup Equations, Bull. Acad. Stiinte Repub. Mold. Mat., 1(80)(2016), pp. 41-63. · Zbl 1349.20069 |
| [68] | Z. ´Esik, A Cayley theorem for ternary algebras. Int. J. Algebra Comput. 8(3)(1998), pp. 311-316. · Zbl 0939.06009 |
| [69] | T.Evans,UniversalalgebraandEuler’sofficerproblem. Amer.Math.Monthly 86(1979), pp. 466-473. · Zbl 0431.05008 |
| [70] | M. C. Fitting, Bilattices in logic programming. in: G. Epstein ed., Proc. 20th Internat. Symp. on Multi-Valued Logic, IEEE, New York, (1990), pp. 63-70. |
| [71] | L. Fuchs, Infinite Abelian Groups, Volume II, Academic Press, New York and London, 1973. · Zbl 0257.20035 |
| [72] | B. Ganter, H. Werner, Equational classes of Steiner systems. Algebra Universalis. 5(1975), pp. 125-140. · Zbl 0312.08002 |
| [73] | G. Gargov, Knowledge, Uncertainty and ignorance in logic: Bilattices and beyond. J. Appl. Non-Classical Logics 9(2-3)(1999), pp. 195-283. · Zbl 0993.03079 |
| [74] | P. S. Gevorgyan, On binary G-spaces. Math.Notes 96(4)(2014), pp. 600-602. · Zbl 1315.54027 |
| [75] | M. L. Ginsberg, Bilattices. Preprint 1986. |
| [76] | M. L. Ginsberg, Multi-valued logics. Preprint 1986. |
| [77] | M. L. Ginsberg, Multi-valued inference. Preprint 1986. |
| [78] | M. L. Ginsberg, Multi-valued logics: a uniform approach to reasoning in artificial intelligence. Computational Intelligence 4, 265-316(1988), pp. 265-316. |
| [79] | B. N. Givens, K. Linton, A. Rosin, L. Dishman, Interassociates of the free commutative semigroup on n generators. Semigroup Forum 74(2007), pp. 370-378. · Zbl 1122.20029 |
| [80] | B. N. Givens, A. Rosin, K. Linton, Interassociates of the bicyclic semigroup. Semigroup Forum 94(2017), pp. 104-122. · Zbl 1422.20028 |
| [81] | A. B. Gorbatkov, Interassociates of a free semigroup on two generators. Mat. Stud. 41(2014), pp. 139-145. · Zbl 1312.20053 |
| [82] | A. B. Gorbatkov, Interassociates of the free commutative semigroup. Sib. Math. J. 54(3), pp. 441-445. · Zbl 1273.20058 |
| [83] | M. Gould, K. A. Linton, A. W. Nelson, Interassociates of monogenic semigroups. Semigroup Forum 68(2004), pp. 186-201. · Zbl 1059.20056 |
| [84] | M. M. Glukhov, Some applications of quasigroups in cryptography. Prikl. Diskr. Math., 2(2)(2008), pp. 28-32. · Zbl 1448.94198 |
| [85] | E. Graczynska,Algebras of M-solid quasivarieties, Siatras International Bookshop, Athens, 2014. · Zbl 1294.08001 |
| [86] | E.Graczynska,OntheproblemonM-hyperquasivarieties, arXiv:math/06096000v3 [math.GM], 2007. |
| [87] | E. Graczynska, D. Schweigert, Hypervarieties of a given type. Algebra Universalis 27(1990), pp. 305-318. · Zbl 0715.08002 |
| [88] | E. Graczynska, R. P¨oschel, M. V. Volkov, Solid pseudovarieties. In.: General algebra and applications in discrete mathematics, ShakerVerlag, Aachen, (1997), pp. 93-100. · Zbl 0923.08004 |
| [89] | G. Gr¨atzer, A theorem on doubly transitive permutation groups with aplication to universal algebra. Fund. Math. 53(1963), pp. 25-41. · Zbl 0218.08005 |
| [90] | G. Gr¨atzer, Two Mal’tsev-type theorems in universal algebra. J. Combinatorial theory 8(1970), pp. 334-342. · Zbl 0194.01401 |
| [91] | G. Gr¨atzer, Universal Algebra, 2nd ed., Springer-Verlag, 1979. · Zbl 0412.08001 |
| [92] | G. Gr¨atzer, Lattice Theory: Foundation, Springer Basel AG, 2011. · Zbl 1233.06001 |
| [93] | H. Gumashyan, On {2,3}-hyperidentities in the invertible {2,3}algebras with a ternary group-operation. J. Contemp. Math. Anal. 45(3)(2010), pp. 47-56. · Zbl 1299.20096 |
| [94] | H. P. Gumm, A cancellation theorem for finite algebras. Colloquia Math. Soc., J.Bolyai 29(1977), pp. 341-344. · Zbl 0483.08003 |
| [95] | M. Hall (Jr.), The theory of groups, New York, 1959. · Zbl 0084.02202 |
| [96] | M. Hall, On a theorem of Jordan. Pacific J. Math. 4:2(1954), pp. 291-226. |
| [97] | P. J. Higgins, Algebras with a scheme of operators. Math. Nachr., 27(1963), pp. 115-132. · Zbl 0117.25903 |
| [98] | N. J. S. Hughes, A theorem on isotopic groupoids. J. London Math. Soc., 32(1957), pp. 510-511. · Zbl 0082.02303 |
| [99] | L. Humberstone, Note on Extending Congruential Modal Logics. Notre Dame Journal of Formal Logic 57(1)(2016), pp. 95-100. · Zbl 1350.03018 |
| [100] | J. Hyndman, R. McKenzie, W. Taylor, k-ary monoids of term operations. Semigroup Forum 44(1992), pp. 31-52. · Zbl 0790.08002 |
| [101] | K. Iseki, A way to BCK and related systems. Math. Japonica 5(2000), pp. 163-170. · Zbl 0978.06012 |
| [102] | K. Iseki, Sh. Tanaka, An introduction to the theory of BCK-algebras. Math. Japonica 23(1978), pp. 1-26. · Zbl 0385.03051 |
| [103] | J. Jakubik, M. Kolibiar, Lattices with a third distributive operation. Math. Slovaca 27(1977), pp. 287-292. · Zbl 0391.06007 |
| [104] | J. Je˘zek, T. Kepka, P. N˘emec, Distributive groupoids, Praha,1981. · Zbl 0484.20031 |
| [105] | B. Jonsson,Varieties of relation algebras. Algebra Universalis 15(1982), pp. 273-298. · Zbl 0545.08009 |
| [106] | B. Jonsson,Congruence distributive varieties. Math. Japonica 42(1995), pp. 353-401. · Zbl 0841.08004 |
| [107] | B. Jonsson, A. Tarski, Representation problems for relation algebras. Bull. Amer. Math. Soc. 54(1948), pp. 80-80. |
| [108] | C. Jordan, Recherches sur les substitutions. J. Math. Pures Appl. 2(17)(1872), pp. 351-363. · JFM 04.0055.01 |
| [109] | J. A. Kalman, Lattices with involution. Trans. Amer. Math. Soc. 87(1958), pp. 485-491. · Zbl 0228.06003 |
| [110] | M. I. Kargapolov, Yu. I. Merzlyakov, Foundation of group theory, Nauka, Moscow, 1977 (in Russian). · Zbl 0499.20001 |
| [111] | H. Karzel, Inzidenzgruppen. Lecture Notes by Pieper, I. and Sorensen, K., University of Hamburg, (1965), pp. 123-135. |
| [112] | T. Kepka, Distributive Steiner quasigroups of order 35. Comment. Math. Univ. Carolinae 195, (1978), pp. 389-401. · Zbl 0373.20062 |
| [113] | W. Kerby, Uber eine scharf 3-fach transitiven Gruppen zugeordnete algebraische Structur. Abh. Math. Sem. Univ. Hamburg 37, (1972), pp. 225-235. · Zbl 0258.17010 |
| [114] | A. Knoebel, A. Romanowska, Distributive Multisemilattices. Dissertationes Mathematicae, Rozprawy Marhematyczne, 1991, Warszawa. · Zbl 0719.06002 |
| [115] | S. R. Kogalovskii, On multiplicative semigroups of rings. Dokl. Akad. Nauk SSSR, 140(1961), pp. 1005-1007.(in Russian) · Zbl 0118.25303 |
| [116] | J. Koppitz, K. Denecke, M-Solid Varieties of Algebras, Springer, 2006. · Zbl 1094.08001 |
| [117] | A. D. Korshunov, Monotone boolean functions. Russian Math. Surveys 58(5)(2003), pp. 928-1001. · Zbl 1072.06008 |
| [118] | H. V. Krainichuk, Classification of group isotopes according to their symmetry groups. Folia Mathematica, 19(1)(2017), pp. 84-98. · Zbl 1396.20080 |
| [119] | A.Krape˘z,Functionalequationsofgeneralizedassociativity,bisymmetry,transitivityanddistributivity.Publ.Inst. Math.(Beograd),30(1981), pp. 81-87. · Zbl 0508.39013 |
| [120] | A. Krape˘z, Generalized associativity on groupoids. Publ. Inst. Math. (Beograd) 28(1980), pp. 105-112. · Zbl 0503.20022 |
| [121] | A. Krape˘z, Cryptographically Suitable Quasigroups via Functional Equations. In: S.Markovski and M.Gusev (Eds.): ICT Innovations 2012, AISC 207,Springer-Verlag, Berlin, Heidelberg, (2013), pp. 264274. |
| [122] | A. Krape˘z, Quadratic level quasigroup equations with four variables, I. Publ. Inst. Math. (Beograd)(N.S.) 81(95)(2007), pp. 53-67. · Zbl 1229.39035 |
| [123] | A. Krape˘z, Quadratic level quasigroup equations with four variables, II. Publ. Inst. Math. (Beograd)(N.S.) 93(107)(2013), pp. 29-47. · Zbl 1299.20093 |
| [124] | A. G. Kurosh, Lectures on General Algebra, Chelsea, New York, 1963. |
| [125] | A. G. Kurosh, General Algebra, Nauka, Moscow, 1974. (in Russian) · Zbl 0289.00004 |
| [126] | D. Lau, Functional algebras on finite sets, a basic course on manyvalued logic and clone theory, Springer-Verlag, Berlin Heidelberg, 2006. · Zbl 1105.08001 |
| [127] | F. W. Lawvere, Functorial semantics of algebraic theories. Proc. Nat. Acad. Sci. 50(1963), pp. 869-872. · Zbl 0119.25901 |
| [128] | W. Leissner, Ein Stufenaufbau der Fasthereiche, Fastkorper and Korper aus ihrer multiplikativen Gruppe. Abh. Math. Sem. Univ. 46(1977), pp. 55-89. · Zbl 0373.12014 |
| [129] | J.-L. Loday, M. O. Ronco, Order structure on the algebra of permutations and of planar binary trees, J. Algebraic Combin., 15(2002), pp. 253-270. · Zbl 0998.05013 |
| [130] | J. Luh, On the theory of simple Γ-rings. Michigan Math. J. 16(1969), pp. 65-75. · Zbl 0175.03101 |
| [131] | R. D. Maddux, Some sufficient conditions for the representability of relation algebras. Algebra Universalis, 8(1978), pp. 162-172. · Zbl 0386.03033 |
| [132] | R. D. Maddux, Nonfinite axiomatizability results for cylindric and relation algebras. Journal of Symbolic Logic 54(1989), pp. 951-974 · Zbl 0686.03035 |
| [133] | R. D. Maddux, Introductory course on relation algebras, finitedimensional cylindric algebras, and their interconnections. In: Colloq.Math.Soc. J.Bolyai 54(1991), pp. 361-392. (“Algebraic logic (Budapest,1988)”) North-Holland, Amsterdam. · Zbl 0749.03048 |
| [134] | R. D. Maddux, Finitary algebraic logic. Math. Logic Quart. 39(1993), pp. 566-569. · Zbl 0812.03037 |
| [135] | R. D. Maddux, A perspective on the theory of relation algebras. Algebra Universalis 31(1994), pp. 456-465. · Zbl 0803.03043 |
| [136] | R. D. Maddux, Relation-algebraic semantics. Theoret. Comput. Sci. 160, 1-85(1996), pp. 1-85. · Zbl 0872.68106 |
| [137] | R. D. Maddux, Relation algebras. In “Relational Methods in Computer Science”, Springer-Verlag, Wien, (1997), pp. 22-38. · Zbl 0885.03047 |
| [138] | R. D. Maddux, Relation algebras of formulas. In “Logic at Work”, Physica, Heidelberg, (1999), pp. 613-636. · Zbl 0923.03073 |
| [139] | A. I. Mal’tsev,On the general theory of algebraic systems. Amer.Math.Soc. Translations (2)27(1963), pp. 125-142. · Zbl 0128.02301 |
| [140] | A. I. Mal’tsev, Model correspondences. AMS Selected Translations 23(1959), pp. 313-336. · Zbl 0100.01202 |
| [141] | A. I. Mal’tsev, Some questions of the theory of classes of models. Proceedings of the IVth All-Union Mathematical Congress, 1(1963), pp. 169-198. (in Russian) |
| [142] | A. I. Mal’tsev, Algebraic systems, Springer-Verlag, Berlin-HeidelbergNew York, 1973. · Zbl 0266.08001 |
| [143] | A. I. Mal’tsev, I. A. Mal’tsev, Iterative Post algebras, Nauka, Moscow, 2012. (in Russian) |
| [144] | I. A. Mal’tsev, D. Schveigert, Hyperidentit¨aten von AZ-algebren. Preprint, Fachbereich Mathematik, Universit¨at Kaiserslautern, 1989. |
| [145] | M. Mando, Regular ∀∃(∀)-identities of length four in algebras. Ph.D. Thesis, 1990. Yerevan State University, Yerevan, Armenia. |
| [146] | Yu. I. Manin, Cubic Forms, North-Holland Mathematical Library, Vol 4, 2nd edn. North-Holland, Amsterdam, 1986. · Zbl 0582.14010 |
| [147] | H. B. Mann, The construction of orthogonal Latin squares. Ann. Math. Statist. 13(1942), pp. 418-423. · Zbl 0060.02706 |
| [148] | H. B. Marandjian, On computable solutions to functional equations. CSIT (2011), pp.20-22. |
| [149] | H. B. Marandjian, Selected Topics in Recursive Function Theory in Computer Science, DTH, Lyngby, 1990. |
| [150] | H. B. Marandjian, General Form Recursive Equations I. In: Computer Science Logic. Selected Papers, Lecture Notes in Computer Science, Vol. 933 , Springer, Berlin, Heidelberg, 1995. · Zbl 1044.03530 |
| [151] | E. Marczewski, Independence and homomorphisms in abstract algebras. Fund. Math. 50(1961), pp.45-61. · Zbl 0104.25501 |
| [152] | A. A. Markov, Constructive logic. Uspekhi Mat. Nauk, 5(1950), p.187. (Russian) |
| [153] | V. D. Mazurov, On faithful doubly transitive groups. Problems of Algebra and Logic, Procedeengs of the Siberian Branch of the RAS, 30(1996), pp. 114-118. · Zbl 0912.20002 |
| [154] | V. D. Mazurov, On doubly transitive permutation groups. Siberian Math. J., 31(4)(1990), pp. 778-780. |
| [155] | J. C. C. McKinsey, Postulates for the calculus of binary relations. J. Symbolic Logic, 5(1940), pp. 85-97. · Zbl 0024.00201 |
| [156] | R. N. McKenzie, Representation of relation algebras. Michigan J.Math. 17(1970), pp. 279-287. · Zbl 0191.01102 |
| [157] | R. N. McKenzie, G. F. McNulty, W. T. Taylor, Algebras, lattices, varieties, Volume I, Wadsworth, 1983. · Zbl 0611.08001 |
| [158] | V. G. Melkonian, Quasi-identities and conditional hyperidentities in distributive lattices. Dokl. Akad. Nauk Armenii 94(1993) pp. 195-199. (Russian) |
| [159] | V. G. Melkonian, Circuit integrating through lattice hyperterms. Discrete Mathematics, Algorithms and Applications, 3(2011), pp. 101119. · Zbl 1219.90145 |
| [160] | B. Mobasher, D. Pigozzi, G. Slutzki, Multi-valued logic programming semantics: An Algebraic Approach. Teoretical Computer Science, 171(1997), pp. 77-109. · Zbl 0874.68046 |
| [161] | B. Mobasher, D. Pigozzi, G. Slutzki, G. Voutsadakis, A duality theory for bilattices. Algebra Universalis 43(2000), pp. 109-125. · Zbl 1012.06008 |
| [162] | G. C. Moisil, Recherches sur l’algebre de la logique. Annales scientifiques de l’universite de Jassy 22(1935), pp. 1-117. |
| [163] | C. Moor, Quasi-Linear Cellular Automata. Physica D103(1997), pp. 100-132. Proceedings of the International Workshop on Lattice Dynamics. · Zbl 1194.37023 |
| [164] | R. Moufang, Zur structure von Alternative K¨orpern. Math. Ann. 110(1935), pp. 416-430. · Zbl 0010.00403 |
| [165] | Yu. M. Movsisyan, Biprimitive classes of algebras of second degree. Matematicheskie Issledovania 9(1974), pp. 70-84. (in Russian) |
| [166] | Yu. M. Movsisyan, Hyperidentities of associativity in systems of semigroups. Dokl. Akad. Nauk Arm. SSR 62(1976), pp. 282-286. · Zbl 0371.20048 |
| [167] | Yu. M. Movsisyan, Balanced hyperidentities of length three. Dokl. Akad. Nauk Arm. SSR 76(1983), pp. 55-60. · Zbl 0517.20049 |
| [168] | Yu. M. Movsisyan, Coidentities in algebras. Dokl. Akad. Nauk Arm. SSR 77(1983), pp. 51-54. · Zbl 0538.08001 |
| [169] | Yu. M. Movsisyan, A theorem of Albert in the category of bynary algebras. Dokl. Akad. Nauk Arm. SSR 78(1984), pp. 3-7. · Zbl 0543.08001 |
| [170] | Yu. M. Movsisyan, Introduction to the Theory of Algebras with Hyperidentities, Yerevan State University Press, Yerevan, 1986 (in Russian). · Zbl 0675.08001 |
| [171] | Yu. M. Movsisyan, Hyperidentities and groups. Dokl. Akad. Nauk Arm. SSR 87(1988), pp. 104-105. · Zbl 0674.20039 |
| [172] | Yu. M. Movsisyan, The multiplicative group of a field and hyperidentities. Math. USSR Izv., 35(2)(1990), pp. 377-391. · Zbl 0705.12002 |
| [173] | Yu. M. Movsisyan, Hyperidentities and hypervarieties in algebras, Yerevan State University Press, Yerevan, 1990 (in Russian). · Zbl 0728.08013 |
| [174] | Yu. M. Movsisyan, Hyperidentities of Boolean algebras. Russ. Acad. Sci. Izv. Math. 40(3)(1993), pp. 607-622. · Zbl 0787.08006 |
| [175] | Yu. M. Movsisyan, On a theorem of Schauffler. Math. Notes, 53(1993), pp. 172-179. · Zbl 0816.20066 |
| [176] | Yu. M. Movsisyan, Hyperidentities in the variety of lattices. Math. Notes 59(6)(1996), pp. 686-688. · Zbl 0919.06003 |
| [177] | Yu. M. Movsisyan, Algebras with hyperidentities of the variety of Boolean algebras. Russ. Acad. Sci. Izv. Math. 60(6)(1996), pp. 12191260. · Zbl 0885.08002 |
| [178] | Yu. M. Movsisyan, Hyperidentities in algebras and varieties. Russian Math. Surveys, 53(1)(1998), pp. 57-108. · Zbl 0921.08005 |
| [179] | Yu. M. Movsisyan, Generalization of Toyoda theorem, Loop’s 99, Praha July 27-August 1, (1999), pp. 26-27. |
| [180] | Yu. M. Movsisyan, Hyperidentities and hypervarieties. Sci. Math. Jpn. 54(2001), pp. 595-640. · Zbl 1003.08001 |
| [181] | Yu. M. Movsisyan, Boolean Bisemigroups, Bigroups and Local Bigroups. Computer Science and Information Technologies, Proceedings of the Conference, (2005), pp. 97-104. |
| [182] | Yu.M.Movsisyan,OntherepresentationsofDeMorgan algebras.TrendsinlogicIII,Studialogica,Warsaw,2005, http://www.ifispan.waw.pl/studialogica/Movsisyan.pdf |
| [183] | Yu. M. Movsisyan, Binary representation of algebras with at most two binary operations. A Cayley theorem for distributive lattices. Internat. J. Algebra Comput. 19(1)(2009), pp. 97-106. · Zbl 1174.06006 |
| [184] | Yu. M. Movsisyan, Bilattices and hyperidentities. Proc. Steklov Inst. Math. 274(1)(2011), pp. 174-192. · Zbl 1294.06007 |
| [185] | Yu. M. Movsisyan, Interlaced, modular, distributive and Boolean bilattices. Armen. J. Math. 1(3)(2008), pp. 7-13. · Zbl 1281.06005 |
| [186] | Yu. M. Movsisyan, Hyperidentities and Related Concepts, I. Armen. J. Math. 2(2017), pp. 146-222. · Zbl 1404.08001 |
| [187] | Yu. M. Movsisyan, V. A. Aslanyan, Hyperidentities of De Morgan algebras. Log. J. IGPL 20(2012), pp. 1153-1174. · Zbl 1276.06005 |
| [188] | Yu. M. Movsisyan, V. A. Aslanyan, Algebras with hyperidentities of the variety of De Morgan algebras. J. Contemp. Math. Anal. 5(2013), pp. 233-240. · Zbl 1302.06015 |
| [189] | Yu. M. Movsisyan, V. A. Aslanyan, Subdirectly irreducible algebras with hyperidentities of the variety of De Morgan algebras. J. Contemp. Math. Anal. 6(2013), pp. 241-246. · Zbl 1302.06016 |
| [190] | Yu. M. Movsisyan, V. A. Aslanyan, A functional completeness theorem for De Morgan functions. Discrete Appl. Math. 162(2014), pp. 1-16. · Zbl 1338.06011 |
| [191] | Yu. M. Movsisyan, V. A. Aslanyan, De Morgan Functions and Free De Morgan Algebras. Demonstratio Math. 2(2014), pp. 271-283. · Zbl 1315.06012 |
| [192] | Yu. M. Movsisyan, V. A. Aslanyan, Boole-De Morgan algebras and quasi-De Morgan functions. Comm. Algebra 42(2014), pp. 4757-4777. · Zbl 1338.06010 |
| [193] | Yu. M. Movsisyan, V. A. Aslanyan, Super-Boolean functions and free Boolean quasilattices. Discrete Math. Algorithms Appl. 6(2014), pp. 1450024(13 pages). · Zbl 1312.06010 |
| [194] | Yu. M. Movsisyan, V. A. Aslanyan, Super-De Morgan functions and free De Morgan quasilattices. Cent. Eur. J. Math. 12(2014), pp. 17491761. · Zbl 1346.08004 |
| [195] | Yu. M. Movsisyan, A. G. Barkhudaryan, On hypervarieties of QBalgebras. Proceedings of the YSU, Phisics and Mathematics 2(1996), pp. 16-24. |
| [196] | Yu. M. Movsisyan, L. M. Budaghyan, The elementary characterization of algebras with hyperidentities of Boolean algebras. International conference “Mathematical Logic, Algebra And Set Theory” dedicated to the 100th anniversary of P.S.Novikov, August 27-31, 2001. |
| [197] | Yu. M. Movsisyan, L. M. Budaghyan, On elementary decidability of quasi-Boolean algebras. International Conference “Mathematics in Armenia, Advances and Perspectives”, September 30 - October 7, Yerevan, (2003), pp. 65-67. |
| [198] | Yu. M. Movsisyan, L. M. Budaghyan, V. A. Aslanyan, De Morgan and bi-De Morgan functions (manuscript). |
| [199] | Yu. M. Movsisyan, S. S. Davidov, Algebras that are nearly quasigroups, Moscow, LENAND, 2018 (in Russian). |
| [200] | Yu. M. Movsisyan, S. S. Davidov, M. Safaryan, Constraction of free g-dimonoids. Algebra Discrete Math., 18(2014), pp. 140-150. · Zbl 1333.08005 |
| [201] | Yu. M. Movsisyan, D. S. Davidova, Representation theorem for interlaced q-bilattices. Logic, Algebra and Truth Degrees, 10-14 September 2012, Kanazawa, Ishikawa, Japan, JAIST, (2012), pp. 110-113. |
| [202] | Yu. M. Movsisyan, D. S. Davidova, Hyperidentities of weakly idempotent lattices. J. Contemp. Math. Anal. 6(2015), pp. 259-264. · Zbl 1341.06008 |
| [203] | Yu. M. Movsisyan , D. S. Davidova, A set-theoretical representation for weakly idempotent lattices and interlaced weakly idempotent bilattices. European Journal of Mathematics 2(2016), pp. 863-873. · Zbl 1402.06001 |
| [204] | Yu. M. Movsisyan, T. A. Hakobyan, Associative nontrivial hyperidentities in semigroups. J. Contemp. Math. Anal. 46(3)(2011), pp. 121-130. · Zbl 1299.20065 |
| [205] | Yu. M. Movsisyan, T. A. Hakobyan, Distributive hyperidentities in semigroups. J. Contemp. Math. Anal. 46(6)(2011), pp. 293-298. · Zbl 1299.20064 |
| [206] | Yu. M. Movsisyan, T. A. Hakobyan, Artin theorem for semigroups. J. Algebra Appl. 16(2)(2017), pp. 1750034(16 pages). · Zbl 1398.20071 |
| [207] | Yu. M. Movsisyan, V. G. Melkonian, On hyperidentities of distributive lattices. Dokl. Akad. Nauk Armenii 95(1995), pp. 75-78. |
| [208] | Yu. M. Movsisyan, E. Nazari, A Cayley theorem for the multiplicative semigroup of a field. J. Algebra Appl. 11(2)(2012), pp. 1-12. · Zbl 1269.20055 |
| [209] | Yu. M. Movsisyan, E. Nazari, Transitive Modes. Demonstratio Math. 44(3)(2011), pp. 511-522. · Zbl 1237.08001 |
| [210] | Yu. M. Movsisyan, J. Pashazadeh, Characterization of binary polynomials of idempotent algebras. J. Math. Sci. (N.Y.) 186(5)(2012), pp. 802-804. · Zbl 1284.08010 |
| [211] | Yu. M. Movsisyan, A. B. Romanowska, J. D. H. Smith, Hyperidentities and Ginsberg-Fitting type theorems. Eighteenth Midwest Conference on Combinatorics, Cryptography, and Computing, October 28-30, 2004, Rochester, New York. |
| [212] | Yu. M. Movsisyan, A. B. Romanowska, J. D. H. Smith, Superproducts, hyperidentities, and algebraic structures of logic programming. J. Combin. Math. Combin. Comput., 58(2006), pp. 101-111. · Zbl 1108.68028 |
| [213] | Yu. M. Movsisyan, I. R. Simonyan, Hyperidentities of distributivity in varieties of semigroups. Computer Science and Infofmation Technologies, Yerevan, (1999), pp.24-26. |
| [214] | Yu. M. Movsisyan, V. Toghanyan, On t-stochastic algebras. Aequationes Math. 76(2008), pp. 241-248. · Zbl 1159.08003 |
| [215] | Yu. M. Movsisyan, V. Toghanyan, On De Morgan Bimonoids. Computer Science and Information Technologies, Proceedings of the Conference,(2007), pp. 57-57. |
| [216] | W. D. Neumann, Malcev conditions, spectra and Kronecker product. J. Austral. Math. Soc. 25(1978), pp. 103-117. · Zbl 0387.08004 |
| [217] | N. Nobusawa, On a generalization of the ring theory. Osaka J. Math. 1(1964), pp. 81-89. · Zbl 0135.02701 |
| [218] | R. Padmanabhan, P. Penner, Bases of hyperidentities of lattices and semilattices. C.R. Math. Rep. Acad. Sci. Canada 4(1982), pp. 9-14. · Zbl 0478.06004 |
| [219] | R. Padmanabhan, P. Penner, Binary hyperidentities of lattices. Aequationes Math. 44(1992), pp. 154-167. · Zbl 0761.08002 |
| [220] | R. Padmanabhann, P. Penner, Lattice ordered polynomial algebras. Order 15(1998), pp. 75-86. · Zbl 0912.06010 |
| [221] | G. Paseman, A small basis for Hyperassociativity. Preprint, Berkley, 1993. |
| [222] | G. Paseman, On Two Problems From “Hyperidentities and Clones”. 2014, arxiv.org/abs/1408.XXXX. |
| [223] | J. Pashazadeh, A characterization of De Morgan bisemigroup of binary functions. Internat. J. Algebra Comput. 18(5)(2008), pp. 951-956. · Zbl 1158.06005 |
| [224] | P. Penner, Hyperidentities of semilattices. Houston J. Math. 10(1984), pp. 81-108. · Zbl 0537.06005 |
| [225] | T. Pirashvili, Sets with two associative operations, Cent. Eur. J. Math. 2(2003), pp. 169-183. · Zbl 1032.16032 |
| [226] | H. Pflugfelder, Quasigroups and Loops, Introduction, Heldermann Verlag, Berlin, 1990. · Zbl 0715.20043 |
| [227] | A. G. Pinus, Foundations of universal algebra, Novosibirsk State Technical University, Novosibirsk, 2005. (Russian) |
| [228] | J. Plonka, On hyperidentities of some varieties. General Algebra and Discrete Mathematics. V.21. Lemgo: Helderman Verlag. Res. Exposition Math.(1995). pp. 199-213. · Zbl 0813.08004 |
| [229] | J. Plonka, A. B. Romanowska, Semilattice sums. In Universal Algebra and Quasigroup Theory, (eds. A.Romanowska, J.D.H.Smith),(1992), pp. 123-158. Helderman Verlag, Berlin. · Zbl 0802.08001 |
| [230] | B. I. Plotkin, Automorphisms groups of algebraic systems, Nauka, Moscow, 1966. (Russian) |
| [231] | B. I. Plotkin, Universal algebra, algebraic logic, and databases, Kluwer Academic Publisher, 1994. · Zbl 0785.68025 |
| [232] | L. Pol´ak, On hyperassociativity. Algebra Universalis 36(1996), pp. 293-300. |
| [233] | L. Pol´ak, All Solid Varieties of Semigroups. J. Algebra 219(1999), pp. 421-436. · Zbl 0935.20050 |
| [234] | L. S. Pontryagin, Continuous groups, Nauka, Moscow, 1973. (Russian) |
| [235] | E. Post, Introduction to a general theory of elementary propositions. Amer. J. Math. 43(1921), pp. 163-185. · JFM 48.1122.01 |
| [236] | E. Post, Two-valued iterative systems of mathematical logic. Annals of Math. Studies, 5(1941), Prinseton Univ. Press, Princeton-London. · Zbl 0063.06326 |
| [237] | H. A. Priestley, Distributive bilattices and their cousins: representation via natural dualities. Research Workshop on Duality Theory in Algebra, Logic and Computer Science, University of Oxford, June 1314, (2012), pp. 18-18. |
| [238] | J. H. Przytycki, Knot and distributive homology: from arc colorings to Yang-Baxter homology. In: New Ideas in Low Dimensional Topology, (2015), pp. 413-488. · Zbl 1323.57010 |
| [239] | A. Pynko,Regular bilattices. J. Applied Non-Classical Logics 10(2000), pp. 93-111. · Zbl 1031.06005 |
| [240] | R. W. Quackenbush, Varieties of Steiner loops and Steiner quasigroups. Can.J.Math. 28(1976), pp. 1187-1198. · Zbl 0359.20070 |
| [241] | H. Rasiowa,An algebraic approach to non-classical logics, NortHolland Publ. Co., Amsterdam, 1974. · Zbl 0299.02069 |
| [242] | M. Reichel, Bi-homomorphismen und Hyperidentitaten. Dissertation, University Potsdam, 1994. |
| [243] | B.Richter,Dialgebren,DoppelalgebrenundihreHomologie, Diplomarbeit,UniversitatBonn(1997).http:/www.math.unihamburg.de/home/richter/publications.html. |
| [244] | A. B. Romanowska, J. D. H. Smith, Modal theory, Helderman-Verlag, Berlin, 1985. · Zbl 0553.08001 |
| [245] | A. B. Romanowska, J. D. H. Smith, Modes, World Scientific, Singapore, 2002. · Zbl 1012.08001 |
| [246] | A. B. Romanowska, A. Trakul, On the structure of some bilattices. Universal and Applied Algebra (K.Hatkowska, B.Stawski, eds.) World Scientific (1989), pp. 235-253. · Zbl 0738.06008 |
| [247] | I. G. Rosenberg, La structure des fonctions de plusieurs variables sur un ensemble fini. C.R. Acad. Sci. Paris, Ser. A.B. 260(1965), pp. 38173819. · Zbl 0144.01002 |
| [248] | G. Sabbagh, How not to characterize the multiplicative groups of fields. J. London Math. Soc. 1(1969), pp. 369-370. · Zbl 0184.01301 |
| [249] | A. Sade, Theorie des systemes demosiens de groupoides. Pacific Journal of Mathematics 10(1960), pp. 625-660. · Zbl 0094.24104 |
| [250] | A. Sade, Groupoides en relation associative et semigroupes mutuellements associatifs. Ann. Soc. Sci. Bruxelies 1(75)(1961), pp. 52-57. · Zbl 0102.01703 |
| [251] | H. P. Sankappanavar, A characterization of principal congruences of De Morgan algebras and its applications. Math Logic in Latin America, Proc. IV Latin Amer.Symp.Math.Logic, Santiago, (1978), pp. 341-349. North-Holland Pub. Co., Amsterdam, 1980. · Zbl 0426.06008 |
| [252] | H. P. Sankappanavar, Decision Problems: History and Methods. In A.I.Arruda, N.C.A.da Costa, and R. Chuaqui, eds., Mathematical logic: Proceedings of the First Brazilian Conference, Marcel Dekker, New York, (1978), pp. 241-290. · Zbl 0385.03011 |
| [253] | R. Schauffler, Eine Anwendung zyklischer Permutationen and ihre Theorie. Ph.D. Thesis, Marburg University, 1948. |
| [254] | R. Schauffler, Uber die Bildung von Codew¨ortern. Arch. elekt. Uebertragung 10(1956), pp. 303-314. · Zbl 0070.01203 |
| [255] | R. Schauffler, Die Associativit¨at im Ganzen, besonders bei Quasigruppen. Math. Z., 67(1957), pp. 428-435. · Zbl 0077.24703 |
| [256] | D. Schweigert, Hyperidentities. Algebras and Orders, Kluwer Academic Publishers, Dordrecht Boston, London, (1993), pp. 405-506. · Zbl 0853.08004 |
| [257] | V. Shcherbacov, Elements of Quasigroup Theory and Applications, Taylor & Francis Group, 2017. · Zbl 1491.20003 |
| [258] | V.A.Shcherbakov,Elementsofquasigrouptheoryand someitsapplicationsincodetheoryandcryptology.2003. (http://www.karlin.mff.cuni.cz/ drapal/speccurs.pdf) |
| [259] | M. K. Sen, On Γ-semigroup. In: Algebra and Its Applications (New Delhi, 1981). Lecture Notes in Pure and Appl. Math., 91(1984), pp. 301-308. Dekker, New York. · Zbl 0534.00007 |
| [260] | J. R. Senft, On weak automorphisms of universal algebras. Dissertationes Math., Rozprawy Mat., 74(1970). · Zbl 0211.03001 |
| [261] | M. K. Sen, N. K. Saha, On Γ-semigroup-I. Bull. Calcutta Math. Soc. 78(1986), pp. 180-186. · Zbl 0601.20063 |
| [262] | A. Seth, Γ-group congruences on regular Γ-semigroups. Int. J. Math. Math. Sci. 15(1)(1992), pp. 103-106. · Zbl 0746.20051 |
| [263] | I. P. Shestakov, A. I. Shirshov, A. M. Sli´nko, K. A. Zhevlakov, Rings that are nearly associative. Academic Press, New York, 1982. · Zbl 0487.17001 |
| [264] | J. Sichler, Weak automorphisms of universal algebras. Algebra Universalis 3(1973), pp. 1-7. · Zbl 0273.08008 |
| [265] | I. R. Simonyan, Lattices of distributive and hyperdistributive varieties of semigroups. Proceedings of the YSU, Phisics and Mathematics, 2(2004), pp. 7-19. · Zbl 1347.20065 |
| [266] | L. A. Skornyakov, Stochastic algebra. Soviet Math. (Iz. Vuz. Matematika), 29(7)(1985), pp. 1-12. · Zbl 0593.08002 |
| [267] | J. Slominski, On the satisfiabilities and varieties for abstract algebras induced by the cones and functor dinamics. Demonstratio Math., 26(1993), pp. 11-22. · Zbl 0788.08009 |
| [268] | D. M. Smirnov, Varieties of algebras, Nauka, Novosibirsk, 1992 (in Russian). · Zbl 0778.08003 |
| [269] | J. D. H. Smith, Malcev varieties, Lecture notes in Mathematics 554(1976), Springer Verlag, Berlin New-York. · Zbl 0344.08002 |
| [270] | J. D. H. Smith, Finite codes and groupoid words. European J. Combin., 12(1991), pp. 331-339. · Zbl 0757.20020 |
| [271] | J. D. H. Smith, An Introduction to Quasigroups and Their Representations, Chapman & Hall/Crc, 2006. |
| [272] | J. D. H. Smith, On groups of hypersubstitutions, Algebra Universalis, 64(2010), pp. 39-48. · Zbl 1216.08001 |
| [273] | J. D. H. Smith, Belousov’s Theorem and the quantum Yang-Baxter equation, Buletinul Academiei de Stiinte a Republicii Moldova, 1(80)(2016), pp. 723. · Zbl 1349.20074 |
| [274] | J. D. H. Smith, A. B. Romanowska, Post-Modern Algebra, Wiley, New York, 1999. · Zbl 0946.00001 |
| [275] | E. Sperner, Ein Satz uber Untermengen einer endlichen Menge. Math.Z. 27(1928), pp. 544-548. · JFM 54.0090.06 |
| [276] | S. K. Stein, On the foundation of quasigroups. Trans. Amer. Math. Soc. 85(1957), pp. 228-256. · Zbl 0079.02402 |
| [277] | J. Steiner, Combinatorische aufgabe. J. Reine Angew. Math. 45(1853), pp. 181-182. · ERAM 045.1224cj |
| [278] | A. Suschkewitsch, Generalized group theory, Kiev, 1937. (in Russian) |
| [279] | A. Szendrei, Clones in universal algebra, Les presses de L’universite de Montreal, 1986. · Zbl 0603.08004 |
| [280] | Z. Szylicka, Hyperidentities of some generalizations of lattices. Algebra Universalis 39(1998), pp. 1-29. · Zbl 0934.08006 |
| [281] | A. Tarski, On the calculus of binary relations. J. Symbolic Logic 6(1941), pp. 73-89. · Zbl 0026.24401 |
| [282] | A. Tarski, A. Mostowski, R. Robinson, Undecidable Theories, NorthHolland, Amsterdam, 1953. · Zbl 0053.00401 |
| [283] | W. Taylor, Characterizing Mal’tsev conditions. Algebra Universalis 3, 351-397(1973), pp. 351-397. · Zbl 0304.08003 |
| [284] | W. Taylor, Mal’tsev conditions and spectra. J. Austral. Math. Soc. 29(1980), pp. 143-152. · Zbl 0439.08005 |
| [285] | W. Taylor, Hyperidentities and hypervarieties. Aequationes Math., 23(1981), pp. 30-49. · Zbl 0491.08009 |
| [286] | W. Taylor, Abstract clone theory. Algebras and Orders, Kluwer Academic Publishers, Dordrecht Boston, London,(1993), pp. 507-530. · Zbl 0792.08005 |
| [287] | J. Tits, Sur les groupen doublement transitif continus. Comment. Math. Helv. 26(1952), pp. 203-224. · Zbl 0047.26002 |
| [288] | V. H. Toghanyan, Subdirectly irreducible algebras with various equations. Aequationes Math. 68(2004), pp. 98-107. · Zbl 1055.08003 |
| [289] | K. Toyoda, On axioms of linear functions, Proc. Imp. Acad. Tokyo, 17(1941), pp. 221-227. · Zbl 0061.02403 |
| [290] | T. Traczyk, Weak isomorphisms of Boolean and Post algebras. Colloq. Math. 13(2)(1965), pp. 159-164. · Zbl 0133.24404 |
| [291] | V. Trnkova, Amazingly extensive use of Cook continuum. Math. Japonica 51(2000), pp. 499-549. · Zbl 0955.54011 |
| [292] | K. Urbanik, On algebraic operations in idempotent algebras. Colloquium Math. XIII(1965), pp. 129-157. · Zbl 0132.25903 |
| [293] | J. Uˇsan, Globally associative systems of n-ary quasigroups. Publ. Inst. Math. (Beograd) 19(1975), pp. 155-165. · Zbl 0347.20041 |
| [294] | J. Uˇsan, Description of Super Associative Algebras with n-Quasigroup Operations. Math. Morav. 5(2001), pp. 129-157. · Zbl 1034.20061 |
| [295] | J. Uˇsan, n-Groups in the light of the neutral operations, Electronic version (2006). |
| [296] | J. Uˇsan, M. ˇZiˇzovi´c, n-ary analogy of Schauffler theorem. Publ. Inst. Math. (Beograd) 19(1975), pp. 167-172. · Zbl 0347.20042 |
| [297] | F. W. Wilke, Pseudo-fields and doubly transitive groups. Bull. Austral. Math. Soc. 7(1972), pp. 163-168. · Zbl 0261.12106 |
| [298] | S. L. Wismath, Hyperidentity bases for rectangular bands and other semigroup varieties. J. Austrral. Math. Soc. (Ser. A) 55(1993), pp. 270-286. · Zbl 0816.20053 |
| [299] | S. L. Wismath, A basis for the type < n > hyperidentities of the medial variety of semigroups. Aequationes Math. 49(1995), pp. 205-213. · Zbl 0830.20081 |
| [300] | Yu. I. Yanov, A. A. Muchnik, On the existence of k-valued closed classes withoth a finite basis. Dokl. Acad. Nauk SSSR 127(1959), pp. 44-46.(in Russian) · Zbl 0100.01001 |
| [301] | Yu. L. Yershov, Decidability problems and cunstractive models, Nauka, Moscow,1980.(in Russian) |
| [302] | K. A. Zaretskii, An abstract characterization of the bisemigroup of binary operations. Math. Notes, 1(5)(1967), pp. 347-350. · Zbl 0178.01202 |
| [303] | D. ˇZarkov, A remark on globally associative systems of n-quasigroups over Q = 1, 2, 3, 4. Publ. Inst. Math. (Beograd) 21(1977), pp. 207-211. · Zbl 0361.20068 |
| [304] | H. Zassenhaus, Uber endliche Fastkorper. Abh. Math. Sem. Univ. Hamburg 11(1935/36), pp. 187-220. · JFM 61.0126.01 |
| [305] | H. Zassenhaus, Kennzeichnung endlicher linearer Gruppen als Permutationsgruppen. Abh. Math. Sem. Univ. Hamburg 11(1936), pp. 17-40. · Zbl 0011.24904 |
| [306] | J. L. Zemmer, Near-fields, planar and non-planar. Math. Stud. 31(1964), pp. 145-150. · Zbl 0142.00502 |
| [307] | M. R. ˇZiˇzovi´c, Associative systems of topological n-quasigroups. Algebraic Conference, Novi Sad (1981), pp. 55-60. · Zbl 0497.22004 |
| [308] | A. V. Zhuchok, Free products of doppelsemigroups. Algebra Universalis 76(2016), pp. 355-366. · Zbl 1356.08004 |
| [309] | A.V.Zhuchok,Structureoffreestrongdoppelsemigroups (manuscript). |
| [310] | A. V. Zhuchok, M. Demko, Free n-dinilpotent doppelsemigroups. Algebra Discrete Math., 22(2016), pp. 304-316. · Zbl 1388.08002 |
| [311] | D. Zupnik, On interassociativity and related questions. Aequationes Math. 6(2)(2016), pp. 141-148. · Zbl 0239.08002 |
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