Abstract
Results in the theory of nonassociative rings and related directions reviewed in RZhMatematika during the period 1972–1978 are discussed. Special attention is given to infinite-dimensional Lie algebras, Jordan algebras, alternative rings, Mal'tsev algebras, and varieties, representations, and radicals of nonassociative rings.
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A. A. Lashkhi, “The projection of Magnus rings and Lie algebras,” Sakartvelos Politekhnikuri Instituti, Shromebi, Tr. Gruz. Politekhn. Inst., No. 8 (148), 7–11 (1971).
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A. A. Lashkhi, “Structure isomorphisms of some classes of Lie algebras,” Tbilisis Matematikis fastitutis Shromebi, Sakartvelos SSR Metsnierebata Akademia, Tr. Tbilis. Mat. fast. Akad. Nauk GruzSSR,46, 5–21 (1975).
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R. S. Lipyanskii, “Some radicals of linear Lie algebras,” Usp. Mat. Nauk,29, No. 3, 211–212 (1974).
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R. S. Lipyanskii, “On the algebraic elements in linear Lie algebras,” Uch. Zap. Latv. Univ.,257, No. 2, 52–63 (1976).
R. S. Lipyanskii, “Solvable Lie algebras over a field of characteristic p > 0,” Uch. Zap. Latv. Univ.,204, 72–83 (1974).
I. V. L'vov, “On the finiteness of the basis of identities of some nonassociative rings,” Algebra Logika,14, No. 1, 15–27 (1975).
I. V. L'vov, “Finite-dimensional algebras with infinite bases of identities,” Sib. Mat. Zh.,19, No. 1, 91–99 (1978).
I. V. L'vov, “On varieties generated by finite alternative rings,” Algebra Logika,17, No. 3, 282–286 (1978).
B. O. Makarevich, “Ideal points of semisimple Jordan algebras,” Mat. Zametki,15, No. 2, 295–305 (1974).
Yu. N. Mal'tsev and V. A. Parfenov, “An example of a nonassociative algebra not admitting a finite basis of identities,” Sib. Mat. Zh.,18, No. 6, 1420–1421 (1977).
A. S. Markovichev, “Nil-systems and the radical in alternative Artinian rings,” Mat, Zametki,11, No. 3, 299–306 (1972).
A. S. Markovichev, “On the hereditary property of radicals of rings of type (γ, δ),” Algebra Logika,17, No. 1, 33–55 (1978).
A. S. Markovichev, “Nil-rings of type (γ, δ),” Algebra Logika,17, No. 2, 181–200 (1978).
A. S. Markovichev, “The lower nil-radical of rings of type (γ, δ),” Algebra Logika,17, No. 3, 287–302 (1978).
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N. Ya. Medvedev, “On lattices of varieties of lattice-ordered Lie groups and algebras,” Algebra Logika,16, No. 1, 40–45 (1977).
Ya. A. Medvedev, “Local finiteness of periodic subloops of alternative PI-rings,” Mat. Sb.,103, No. 6, 309–315 (1977).
Yu. A. Medvedev, “The finite-basis property for varieties with a two-term identity,” Algebra Logika,17, No. 6, 705–726 (1978).
Yu. A. Medvedev, “Identities of finite Jordan algebras,” Algebra Logika,18, No. 6, 723–748 (1979).
Yu. A. Medvedev, “An example of a variety of solvable alternative algebras over a field of characteristic 2 which does not have a finite basis of identities,” Algebra Logika,19, No. 3, 300–313 (1980).
I. M. Mikheev, “The locally right-nilpotent radical in the class of right alternative rings,” Algebra Logika,11, No. 2, 174–185 (1972).
I. M. Mikheev, “The Wedderburn theorem on the split-off of the radical for (−1, 1)-algebras,” Algebra Logika,12, No. 3, 298–304 (1973).
I. M. Mikheev, “On prime right alternative algebras,” Algebra Logika,14, No. 1, 56–60 (1975).
I. M. Mikheev, “On the right nilpotence in right alternative rings,” Sib. Mat. Zh.,17, No. 1, 225–227 (1976).
I. M. Mikheev, “On prime right alternative rings,” Algebra Logika,16, No. 6, 682–710 (1977).
I. M. Mikheev, “On prime right alternative rings with an idempotent,” Mat. Zametki,27, No. 2, 185–192 (1980).
S. P. Mishchenko, Varieties of Centrally Metabelian Lie Algebras over a Field of Characteristic Zero, Thesis, Moscow State Univ. (1977).
A. A. Nikitin, “On supernilpotent radicals of (−1, 1)-rings,” Algebra Logika,12, No. 3, 305–311 (1973).
A. A. Nikitin, “Almost alternative algebras,” Algebra Logika,13, No. 5, 501–533 (1974).
A. A. Nikitin, “On the hereditary property of radicals of rings,” Algebra Logika,17, No. 3, 303–315 (1978).
A. A. Nikitin, “On lower radicals of some classes of rings,” Algebra Logika,17, No. 5, 596–610 (1978).
A. Yu. Ol'shanskii, “On some infinite systems of identities,” Tr. Sem. im. I. G. Petrovskogo, No. 3, 139–145 (1978).
B. A. Panferov, “On Lie algebras of maximal class,” Kuban. Univ., Kransnodar (1979) (Manuscript sent to VINITI January 25, 1979, No. 315-79 Dep.).
V. A. Parfenov, “On a property of ideals of free Lie algebras,” Sib. Mat. Zh.,12, No. 1, 171–176 (1969).
V. A. Parfenov, “On exterior differentiations of Lie algebras,” Sib. Mat. Zh.,17, No. 1, 113–118 (1976).
V. A. Parfenov, “On varieties of Lie algebras,” Algebra Logika,6, No. 1, 61–73 (1967).
S. V. Polin, “On identities of finite algebras,” Sib. Mat. Zh.,17, No. 6, 1356–1366 (1976).
S. V. Pchelintsev, “Nilpotence of associators in a free (−1, 1)-ring,” Algebra Logika,13, No. 2, 217–223 (1974).
S. V. Pchelintsev, “A free (−1, 1)-algebra with two generators,” Algebra Logika,13, No. 4, 425–449 (1974).
S. V. Pchelintsev, “Nilpotence of the associator ideal of a finitely generated (−1, 1)-ring,” Algebra Logika,14, No. 5, 543–571 (1975).
S. V. Pchelintsev, “Defining identities of a variety of right alternative algebras,” Mat. Zametki,20, No. 2, 161–176 (1976).
S. V. Pchelintsev, “On a local nilpotent radical in some classes of right alternative rings,” Sib. Mat. Zh.,17, No. 2, 340–360 (1976).
Yu. P. Razmyslov, “The finite-basis property of some varieties of algebras,” Algebra Logika,13, No. 6, 685–693 (1974).
Yu. P. Razmyslov, “On an example of nonsolvable, almost Cross varieties of groups,” Algebra Logika,11, No. 2, 186–205 (1972).
Yu. P. Razmyslov, “On a problem of Kaplansky,” Izv. Akad. Nauk SSSR, Ser. Mat.,37, 483–501 (1973).
Yu. P. Razmyslov, “On a finite basis of identities of a matrix algebra of second order over a field of characteristic zero,” Algebra Logika,121, No. 1, 83–113 (1973).
Yu. P. Razmyslov, “On the Jacobson radical in PI-algebras,” Algebra Logika,13, 337–360 (1974).
Yu. P. Razmyslov, “Trace identities of complete matrix algebras over a field of characteristic 0,” Izv. Akad. Nauk SSSR, Ser. Mat.,38, No. 4, 723–757 (1974).
Yu. P. Razmyslov, “On the Hall-Higman problem,” Izv. Akad. Nauk SSSR, Ser. Mat.,42, No. 4, 833–847 (1978).
E. V. Ritter, “Skeletons of solvable varieties of Lie algebras,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 3, 50–61 (1980).
B. A. Rozenfel'd, R. P. Vyplavina, I. I. Kolokol'tseva, and V. V. Malyutin, “Fractional linear transformations of Jordan algebras,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 5, 169–184 (1974).
B. A. Rozenfel'd and M. P. Zamakhovskii, “Bireductive spaces, simple and quasisimple Jordan algebras,” Tr. Seminara Vektorn. Tenzorn. Analizu Ikh Pril. Geometrii, Mekh. Fiz., Mosk. Univ., No. 16, 251–266 (1972).
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B. A. Rozenfel'd and M. P. Zamakhovskii, “Simple and semisimple Jordan algebras,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 6, 70–77 (1971).
R. É. Roomel'di, “The lower nil-radical of (−1, 1)-rings,” Algebra Logika,12, No. 3, 323–332 (1973).
R. É. Roomel'di, “Nilpotence of ideals in (−1, 1)-rings with a minimal condition,” Algebra Logika,12, No. 3, 333–348 (1973).
R. É. Roomel'di, “Solvability of (−1, 1)-nilrings,” Algebra Logika,12, No. 4, 478–489 (1973).
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A. V. Sidorov, “Solvability and nilpotence in ternary Lie algebras,” Ivanov. Univ., Ivanovo (1976) (Manuscript sent to VINITI, March 22, 1977, No. 1125-77 Dep.).
A. V. Sidorov, “Some properties of ternary Lie algebras,” Ivanov. Univ., Ivanovo (1977) (Manuscript sent to VINITI, September 27, 1977, No. 3795-77 Dep.).
A. V. Sidorov, “On noncommutative ternary Lie algebras,” Algebr. Sistemy, Ivanovo, pp. 81–86.
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V. G. Skosyrskii, “On nilpotence in Jordan and right alternative algebras,” Algebra Logika,18, No. 1, 73–85 (1979).
A. M. Slin'ko, “A remark on radicals and differentiations of rings,” Sib. Mat. Zh.,13, No. 6, 1395–1397 (1972).
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Translated from Itogi Nauki i Tekhniki, Seriya Algebra, Topologiya, Geometriya, Vol. 18, pp 3–72 1981.
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Bakhturin, Y.A., Slin'ko, A.M. & Shestakov, I.P. Nonassociative rings. J Math Sci 18, 169–211 (1982). https://doi.org/10.1007/BF01255614
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DOI: https://doi.org/10.1007/BF01255614