Konstantin Igorevich Beidar (1951-2004). (English. Russian original) Zbl 1151.01321
J. Math. Sci., New York 149, No. 2, 1039-1046 (2008); translation from Fundam. Prikl. Mat. 12, No. 2, 3-15 (2006).
MSC:
| 01A70 | Biographies, obituaries, personalia, bibliographies |
Keywords:
obituaryBiographic References:
Beidar, Konstantin IgorevichReferences:
| [1] | K. I. Beidar, ”The ring of invariants under the action of a finite group of automorphisms of a ring,” Usp. Mat. Nauk, 32, No. 1 (193), 159–160 (1977). · Zbl 0344.16024 |
| [2] | K. I. Beidar and V. D. Ten, ”On the local finiteness of some PI-algebras,” Sib. Mat. Zh., 18, No. 4, 934–938 (1977). · Zbl 0362.16008 |
| [3] | K. I. Beidar, ”Rings with generalized identities. I,” Vestn. Mosk. Univ. Ser. 1 Mat. Mekh., No. 2, 19–26 (1977). · Zbl 0363.16012 |
| [4] | K. I. Beidar, ”Rings with generalized identities. II,” Vestn. Mosk. Univ. Ser. 1 Mat. Mekh., No. 3, 30–37 (1977). · Zbl 0363.16013 |
| [5] | K. I. Beidar, ”Semiprime rings with a generalized identity,” Usp. Mat. Nauk, 32, No. 4 (196), 249–250 (1977). · Zbl 0363.16014 |
| [6] | K. I. Beidar, ”Rings with generalized identities. III,” Vestn. Mosk. Univ. Ser. 1 Mat. Mekh., No. 4, 66–73 (1978). · Zbl 0402.16004 |
| [7] | K. I. Beidar, ”Quotient rings of semiprime rings,” Vestn. Mosk. Univ. Ser. 1 Mat. Mekh., No. 5, 36–43 (1978). · Zbl 0403.16003 |
| [8] | K. I. Beidar, ”Classical rings of quotients of PI-algebras,” Usp. Mat. Nauk, 33, No. 6 (204), 197–198 (1978). · Zbl 0399.16011 |
| [9] | K. I. Beidar, ”Associative rings and finite groups of automorphisms,” Tr. Sem. Petrovsk., No. 4, 33–44 (1978). · Zbl 0416.16012 |
| [10] | K. I. Beidar, A. V. Mikhalev, and K. Salavova, ”Generalized identities and semiprime rings with involution,” Usp. Mat. Nauk, 35, No. 1 (211), 222 (1980). · Zbl 0456.16021 |
| [11] | K. I. Beidar, ”Rings with generalized identities. IV,” Vestn. Mosk. Univ. Ser. 1 Mat. Mekh., No. 4, 3–6 (1980). · Zbl 0463.16006 |
| [12] | K. I. Beidar, ”Modules over commutative semiprime rings,” Mat. Zametki, 29, No. 1, 15–18 (1981). · Zbl 0457.13002 |
| [13] | K. I. Beidar, A. V. Mikhalev, and K. Salavova, ”Generalized identities and semiprime rings with involution,” Math. Z., 178, No. 1, 37–62 (1981). · Zbl 0471.16008 · doi:10.1007/BF01218370 |
| [14] | K. I. Beidar, ”Idempotents in rings with a polynomial identity,” Comment. Math. Univ. Carolin., 22, No. 4, 755–759 (1981). · Zbl 0506.16012 |
| [15] | K. I. Beidar, ”Radicals of finitely generated algebras,” Usp. Mat. Nauk, 36, No. 6 (222), 203–204 (1981). · Zbl 0482.16008 |
| [16] | K. I. Beidar, ”A chain of Kurosh may have an arbitrary finite length,” Czech. Math. J., 32 (107), No. 3, 418–422 (1982). · Zbl 0503.16005 |
| [17] | K. I. Beidar and K. Salavova, ”Some examples of supernilpotent nonspecial radicals,” Acta Math. Acad. Sci. Hungar., 40, No. 1–2, 109–112 (1982). · doi:10.1007/BF01897308 |
| [18] | K. I. Beidar and K. Salavova, ”The lattices of N-radicals, left strong radicals, and left hereditary radicals,” Acta Math. Acad. Sci. Hungar., 42, No. 1–2, 81–95 (1983). · Zbl 0476.16006 |
| [19] | K. I. Beidar, V. N. Latyshev, V. T. Markov, A. V. Mikhalev, L. A. Skornyakov, and A. A. Tuganbaev, Associative rings, J. Sov. Math., 38, 1855–1929 (1987). · Zbl 0621.16001 · doi:10.1007/BF01093433 |
| [20] | K. I. Beidar and A. V. Mikhalev, ”Orthogonal completeness and minimal prime ideals,” Tr. Sem. Petrovsk., No. 10, 227–234 (1984). · Zbl 0569.16011 |
| [21] | K. I. Beidar and A. V. Mikhalev, ”Orthogonal completeness and algebraic systems,” Usp. Mat. Nauk, 40, No. 6 (246), 79–115 (1985). · Zbl 0603.06003 |
| [22] | K. I. Beidar, ”Atoms in the ”lattice” of radicals,” in: Algebras, Rings, and Topologies, Ştiinţe, Kishinev (1985), pp. 21–31. · Zbl 0596.16004 |
| [23] | K. I. Beidar, ”Examples of rings and radicals,” in: Radical Theory (Eger, 1982), Collect. Math. Soc. János Bolyai; Vol. 38, North-Holland, Amsterdam (1985), pp. 19–46. |
| [24] | K. I. Beidar and A. V. Mikhalev, ”Uniform boundedness almost everywhere for orthogonally complete algebraic systems,” Visnik Kiev. Univ. Ser. Mat. Mekh., No. 27, 15–17 (1985). |
| [25] | K. I. Beidar, ”On A. I. Mal’tsev’s theorems on matrix representations of algebras,” Usp. Mat. Nauk, 41, No. 5 (251), 161–162 (1986). |
| [26] | K. I. Beidar, A. V. Mikhalev, and A. M. Slin’ko, ”A primality criterion for nondegenerate alternative and Jordan algebras,” Tr. Mosk. Mat. Obshch., 50, 130–137 (1987). |
| [27] | K. I. Beidar and A. V. Mikhalev, ”The structure of nondegenerate alternative algebras,” Tr. Sem. Petrovsk., No. 12, 59–74 (1987). · Zbl 0653.17015 |
| [28] | K. I. Beidar and A. A. Stolin, ”The Picard group of a projective limit of rings,” in: Operators in Function Spaces and Problems in Function Theory, Naukova Dumka, Kiev (1987), pp. 126–131. · Zbl 0671.13008 |
| [29] | K. I. Beidar and A. V. Mikhalev, ”Semiprime rings with bounded indexes of nilpotent elements,” Tr. Sem. Petrovsk., No. 13, 237–249 (1988). · Zbl 0682.16004 |
| [30] | K. I. Beidar, ”Semisimple classes of algebras and the lower radical,” Mat. Issled., No. 105. (1988), 13–29. · Zbl 0683.17004 |
| [31] | K. I. Beidar and A. V. Mikhalev, ”Additive continuation of derivations of multiplicative semigroups,” in: Mechanics and Applied Mathematics [in Russian], Priok. Knizhn. Izdat., Tula (1988), pp. 112–114. |
| [32] | K. I. Beidar and K. Salavova, ”A class of rings with an essential right socle,” Acta Math. Acad. Sci. Hungar., 53, No. 1–2, 55–59 (1989). · Zbl 0681.16018 |
| [33] | K. I. Beidar, ”The intersection property for radicals,” Usp. Mat. Nauk, 44, No. 1 (265), 187–188 (1989). · Zbl 0678.16004 |
| [34] | K. I. Beidar, S. T. Glavatskii, and A. V. Mikhalev, ”Semisimple classes and lower radicals of topological nonassociative algebras,” Tr. Sem. Petrovsk., No. 14, 250–261 (1989). · Zbl 0699.17005 |
| [35] | K. I. Beidar, S. T. Glavatskii, and A. V. Mikhalev, ”Varieties of topological-groups,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 6, 40–42 (1989). · Zbl 0681.22001 |
| [36] | K. I. Beidar and K. Salavova, ”Additive radicals,” Czech. Math. J., 39 (114), No. 4, 659–673 (1989). · Zbl 0697.16006 |
| [37] | K. I. Beidar and A. V. Mikhalev, ”Generalized Goldie rings. I, II,” in: Abelian Groups and Modules, No. 8, Tomsk. Gos. Univ., Tomsk (1989), 17–34, 35–53. |
| [38] | K. I. Beidar, ”The Andrunakievich lemma and Jordan algebras,” Usp. Mat. Nauk, 45, No. 4 (274), 137–138 (1990). · Zbl 0722.17027 |
| [39] | K. I. Beidar, and K. Trokanova-Salavova, ”On nil rings satisfying minimum condition on principal right ideals,” Acta Math. Acad. Sci. Hungar., 55, No. 3–4, 197–200 (1990). · Zbl 0718.16012 |
| [40] | K. I. Beidar and R. Wiegandt, ”Splitting theorems for nonassociative rings,” Publ. Math. Debrecen, 38, No. 1–2, 121–143 (1991). · Zbl 0726.17003 |
| [41] | V. I. Arnautov, K. I. Beidar, S. T. Glavatskii, and A. V. Mikhalev, ”The intersection property in the theory of radicals of topological algebras,” Tr. Sem. Petrovsk., No. 15, 178–188 (1991). · Zbl 0784.16026 |
| [42] | K. I. Beidar and A. V. Mikhalev, ”On Mal’cev’s theorem on elementary equivalence of linear groups,” in: Proc. Int. Conf. on Algebra (Novosibirsk, 1989), Part 1, Contemp. Math., 131, Part 1, Amer. Math. Soc., Providence (1992), pp. 29–35. · Zbl 0796.20037 |
| [43] | V. I. Arnautov, K. I. Beidar, S. T. Glavatsky, and A. V. Mikhalev, ”Intersection property in the radical theory of topological algebras,” in: Proc. Int. Conf. on Algebra (Novosibirsk, 1989), Part 2, Contemp. Math., 131, Part 2, Amer. Math. Soc., Providence (1992), pp. 205–225. · Zbl 0767.16017 |
| [44] | K. I. Beidar and R. Wisbauer, ”Strictly semiprime modules and rings,” Usp. Mat. Nauk, 48, No. 1 (289), 161–162 (1993). · Zbl 0811.16016 |
| [45] | K. I. Beidar and R. Wiegandt, ”Rings with involution and chain conditions,” J. Pure Appl. Algebra, 87, No. 3, 205–220 (1993). · Zbl 0787.16021 · doi:10.1016/0022-4049(93)90109-7 |
| [46] | K. I. Beidar, ”On essential extensions, maximal essential extensions and iterated maximal essential extensions in radical theory,” in: L. Márki, ed., Theory of Radicals (Szekszárd, 1991), Collect. Math. Soc. János Bolyai, 61, North-Holland, Amsterdam (1993), pp. 17–26. · Zbl 0810.16019 |
| [47] | K. I. Beidar and R. Wiegandt, ”Rings with involution and conditions for bi-ideal chains,” Usp. Mat. Nauk, 48, No. 5 (293), 159–160 (1993). · Zbl 0826.16031 |
| [48] | K. I. Beidar and V. T. Markov, ”A semiprime PI ring which has a faithful module with Krull dimension is a Goldie ring,” Usp. Mat. Nauk, 48, No. 6 (294), 141–142 (1993). · Zbl 0833.16023 |
| [49] | K. I. Beidar, ”Classical quotient rings of semiprime PI-rings,” Algebra Logika, 32, No. 1, 3–16 (1993). · Zbl 0799.16018 |
| [50] | K. I. Beidar and R. Wisbauer, ”Strongly and properly semiprime modules and rings,” in: Ring Theory (Granville, OH, 1992), World Sci. Publishing, River Edge, NJ (1993), pp. 58–94. · Zbl 0853.16021 |
| [51] | K. I. Be@i@dar, E. R. Puczy-lowski, and P. F. Smith, ”Krull dimension of modules over involution rings,” Proc. Amer. Math. Soc., 121, No. 2, 391–397 (1994). · Zbl 0805.16032 |
| [52] | K. I. Beidar, U. Knauer, and A. V. Mikhalev, ”An example of two von Neumann regular rings with nonisomorphic Morita equivalent multiplicative semigroups,” Semigroup Forum, 48, No. 3, 381–383 (1994). · Zbl 0803.16009 · doi:10.1007/BF02573686 |
| [53] | K. I. Beidar, ”On questions of B. J. Gardner and A. D. Sands,” J. Aust. Math. Soc. Ser. A, 56, No. 3, 314–319 (1994). · Zbl 0811.16017 · doi:10.1017/S1446788700035527 |
| [54] | K. I. Beidar, ”Classical localizations of alternative algebras,” J. Math. Sci., 69, No. 3, 1098–1104 (1994). · Zbl 0835.17024 · doi:10.1007/BF01254395 |
| [55] | K. I. Beidar, Y. Fong, and K. P. Shum, ”On the hearts of subdirectly irreducible near-rings,” Southeast Asian Bull. Math., 18, No. 2, 5–9 (1994). · Zbl 0840.16034 |
| [56] | K. I. Beidar, W. S. Martindale, III, and A. V. Mikhalev, ”Lie isomorphisms in prime rings with involution,” J. Algebra, 169, No. 1, 304–327 (1994). · Zbl 0813.16020 · doi:10.1006/jabr.1994.1286 |
| [57] | K. I. Beidar and S. A. Pikhtil’kov, ”On the prime radical of special Lie algebras,” Usp. Mat. Nauk, 49, No. 1 (295), 233 (1994). |
| [58] | K. I. Beidar and R. Wisbauer, ”Properly semiprime self-pp-modules,” Commun. Algebra, 23 (1995), No. 3, 841–861. · Zbl 0822.16017 · doi:10.1080/00927879508825252 |
| [59] | K. I. Beidar, Y. Fong, W.-F. Ke, S.-Y. Liang, ”Nearring multiplications on groups,” Commun. Algebra, 23, No. 3, 999–1015 (1995). · Zbl 0832.16036 · doi:10.1080/00927879508825264 |
| [60] | K. I. Beidar and A. V. Mikhalev, ”The method of orthogonal completeness in the structure theory of rings,” J. Math. Sci., 73, No. 1, 1–46 (1995). · Zbl 0846.16001 · doi:10.1007/BF02366353 |
| [61] | K. I. Beidar and P. Grzeszczuk, ”Actions of Lie algebras on rings without nilpotent elements,” Algebra Colloq., 2, No. 2, 105–116 (1995). · Zbl 0832.16032 |
| [62] | K. I. Beidar and A. V. Mikhalev, ”Anti-isomorphisms of endomorphism rings of modules and the Morita anti-equivalence,” Usp. Mat. Nauk, 50, No. 1 (301), 187–188 (1995). · Zbl 0845.16010 |
| [63] | K. I. Beidar and A. V. Mikhalev, ”On topologization of rings with infinite lower Baer radical,” in: Second Int. Conf. on Algebra (Barnaul, 1991), Contemp. Math., 184, Amer. Math. Soc., Providence, RI (1995), pp. 43–47. |
| [64] | K. I. Beidar and A. V. Mikhalev, ”Generalized polynomial identities and rings that are sums of two subrings,” Algebra Logika, 34, No. 1, 3–11 (1995). · Zbl 0846.16016 |
| [65] | K. I. Beidar, A. V. Mikhalev, and G. E. Puninskii, Logical aspects of the theory of rings and modules, Fundam. Prikl. Mat., 1, No. 1, 1–62 (1995). · Zbl 0892.16001 |
| [66] | K. I. Beidar, W. S. Martindale, III, and A. V. Mikhalev, Rings with Generalized Identities, Monographs and Textbooks in Pure and Applied Mathematics, Vol. 196, Marcel Dekker, New York (1996). · Zbl 0847.16001 |
| [67] | K. I. Beidar, Y. Fong, and C. S. Wang, ”On the lattice of strong radicals,” J. Algebra, 180, No. 2, 334–340 (1996). · Zbl 0848.16014 · doi:10.1006/jabr.1996.0070 |
| [68] | K. I. Beidar, Y. Fong, X. K. Wang, ”Posner and Herstein theorems for derivations of 3-prime near-rings,” Commun. Algebra, 24, No. 5, 1581–1589 (1996). · Zbl 0849.16039 · doi:10.1080/00927879608825656 |
| [69] | K. I. Beidar, Y. Fong, and W.-F. Ke, ”On finite circular planar nearrings,” J. Algebra, 185, No. 3, 688–709 (1996). · Zbl 0863.16038 · doi:10.1006/jabr.1996.0347 |
| [70] | K. I. Beidar, Y. Fong, and W.-F. Ke, ”On the simplicity of centralizer nearrings,” in: First Int. Tainan-Moscow Algebra Workshop (Tainan, 1994), Walter de Gruyter, Berlin (1996), pp. 139–146. · Zbl 0877.16025 |
| [71] | K. I. Beidar, Y. Fong, U. Knauer, A. V. Mikhalev, and K. P. Shum, ”Semigroups with generalized polynomial identities,” in: First Int. Tainan-Moscow Algebra Workshop (Tainan, 1994), Walter de Gruyter, Berlin (1996), pp. 147–157. · Zbl 0869.20041 |
| [72] | K. I. Beidar and A. V. Mikhalev, ”Anti-isomorphisms, induced by Morita anti-equivalences, of endomorphism rings of modules that are close to free,” Tr. Sem. Petrovsk., No. 19, 338–344 (1996). · Zbl 0917.16005 |
| [73] | K. I. Beidar, E. R. Puczy-lowski, and P. F. Smith, ”Krull dimension of modules over involution rings. II,” Proc. Amer. Math. Soc., 125, No. 2, 355–361 (1997). · Zbl 0864.16030 · doi:10.1090/S0002-9939-97-03724-6 |
| [74] | K. I. Beidar, Y. Fong, and A. Stolin, ”On Frobenius algebras and the quantum Yang-Baxter equation,” Trans. Amer. Math. Soc., 349, No. 9, 3823–3836 (1997). · Zbl 0886.16019 · doi:10.1090/S0002-9947-97-01808-4 |
| [75] | K. I. Beidar and R. Wiegandt, ”Radicals induced by the total of rings,” Beitr. Algebra Geom., 38, No. 1, 149–159 (1997). · Zbl 0874.16014 |
| [76] | K. I. Beidar, Y. Fong, and A. A. Stolin, ”On antipodes and integrals in Hopf algebras over rings and the quantum Yang-Baxter equation,” J. Algebra, 194, No. 1, 36–52 (1997). · Zbl 0880.16018 · doi:10.1006/jabr.1996.7019 |
| [77] | K. I. Beidar, Y. Fong, and A. Stolin, ”Symmetric algebras and Yang-Baxter equation,” Rend. Circ. Mat. Palermo (2), Suppl. No. 46 (Proc. 16th Winter School ”Geometry and Physics” (Srní, 1996)), 15–28 (1997). · Zbl 0884.17007 |
| [78] | K. I. Beidar, ”On rings with zero total,” Beitr. Algebra Geom., 38, No. 2, 233–239 (1997). · Zbl 0884.16006 |
| [79] | K. I. Beidar, Y. Fong, P.-H. Lee, and T.-L. Wong, ”On additive maps of prime rings satisfying the Engel condition,” Commun. Algebra, 25, No. 12, 3889–3902 (1997). · Zbl 0898.16013 · doi:10.1080/00927879708826093 |
| [80] | K. I. Beidar, Y. Fong, and W.-F. Ke, ”On complemented radicals,” J. Algebra, 201, No. 1, 328–356 (1998). · Zbl 0911.16013 · doi:10.1006/jabr.1997.7254 |
| [81] | K. I. Beidar, ”On functional identities and commuting additive mappings,” Commun. Algebra, 26, No. 6, 1819–1850 (1998). · Zbl 0901.16011 · doi:10.1080/00927879808826241 |
| [82] | K. I. Beidar and W. S. Martindale, III, ”On functional identities in prime rings with involution,” J. Algebra, 203, No. 2, 491–532 (1998). · Zbl 0904.16012 · doi:10.1006/jabr.1997.7285 |
| [83] | K. I. Beidar and Y. Fong, ”On radicals of monomial algebras,” Commun. Algebra, 26, No. 12, 3913–3919 (1998). · Zbl 0916.16013 · doi:10.1080/00927879808826384 |
| [84] | K. I. Beidar, ”On principally hereditary radicals,” Commun. Algebra, 26, No. 12, 3899–3912 (1998). · Zbl 0919.16013 · doi:10.1080/00927879808826383 |
| [85] | K. I. Beidar, Y. Fong, W.-F. Ke, and W.-R. Wu, ”On semi-endomorphisms of groups,” Commun. Algebra, 27, No. 5, 2193–2205 (1999). · Zbl 0930.16023 · doi:10.1080/00927879908826558 |
| [86] | K. I. Beidar, M. Brešar, and M. A. Chebotar, ”Generalized functional identities with (anti-)automorphisms and derivations on prime rings. I,” J. Algebra, 215, No. 2, 644–665 (1999). · Zbl 0934.16020 · doi:10.1006/jabr.1998.7751 |
| [87] | K. I. Beidar and Y. Fong, ”On additive isomorphisms of prime rings preserving polynomials,” J. Algebra, 217, No. 2, 650–667 (1999). · Zbl 0934.16030 · doi:10.1006/jabr.1998.7833 |
| [88] | K. I. Beidar and R. Wiegandt, ”Radical assignments and radical classes,” Bul. Acad. Ştiinţe Repub. Mold. Mat., No. 2, 17–27 (1999). · Zbl 0946.16013 |
| [89] | K. I. Beidar, Y. Fong, and L. A. Bokut, ”Prime rings with semigroup generalized identity,” Commun. Algebra, 28, No. 3, 1497–1501 (2000). · Zbl 0949.16022 · doi:10.1080/00927870008826909 |
| [90] | K. I. Beidar and M. Brešar, ”Applying the density theorem for derivations to range inclusion problems,” Studia Math., 138, No. 1, 93–100 (2000). · Zbl 0954.16026 |
| [91] | K. I. Beidar, M. Brešar, and M. A. Chebotar, ”Jordan isomorphisms of triangular matrix algebras over a connected commutative ring,” Linear Algebra Appl., 312, No. 1–3, 197–201 (2000). · Zbl 0962.15007 · doi:10.1016/S0024-3795(00)00087-2 |
| [92] | K. I. Beidar, S.-C. Chang, M. A. Chebotar, and Y. Fong, ”On functional identities in left ideals of prime rings,” Commun. Algebra, 28, No. 6, 3041–3058 (2000). · Zbl 0971.16014 · doi:10.1080/00927870008827008 |
| [93] | K. I. Beidar, M. Brešar, M. A. Chebotar, and W. S. Martindale, III, ”On functional identities in prime rings with involution. II,” Commun. Algebra, 28, No. 7, 3169–3183 (2000). · Zbl 1015.16027 · doi:10.1080/00927870008827017 |
| [94] | K. I. Beidar and M. A. Chebotar, ”On functional identities and d-free subsets of rings. I,” Commun. Algebra, 28, No. 8, 3925–3951 (2000). · Zbl 0991.16017 · doi:10.1080/00927870008827066 |
| [95] | K. I. Beidar and M. A. Chebotar, ”On functional identities and d-free subsets of rings. II,” Commun. Algebra, 28, No. 8, 3953–3972 (2000). · Zbl 0991.16018 · doi:10.1080/00927870008827067 |
| [96] | K. I. Beidar and M. A. Chebotar, ”On Lie-admissible algebras whose commutator Lie algebras are Lie subalgebras of prime associative algebras,” J. Algebra, 233, No. 2, 675–703 (2000). · Zbl 0998.16024 · doi:10.1006/jabr.2000.8449 |
| [97] | K. I. Beidar and S. A. Pikhtil’kov, ”The prime radical of special Lie algebras,” Fundam. Prikl. Mat., 6, No. 3, 643–648 (2000). · Zbl 1001.17004 |
| [98] | K. I. Beidar, M. Brešar, and M. A. Chebotar, ”Functional identities on upper triangular matrix algebras,” J. Math. Sci., 102, No. 6, 4557–4565 (2000). · Zbl 1019.16012 |
| [99] | K. I. Beidar and M. A. Chebotar, ”On surjective Lie homomorphisms onto Lie ideals of prime rings,” Commun. Algebra, 29, No. 10, 4775–4793 (2001). · Zbl 1004.16030 · doi:10.1081/AGB-100106785 |
| [100] | K. I. Beidar and F. Kasch, ”Good conditions for the total,” in: Int. Symp. on Ring Theory (Kyongju, 1999), Birkhauser, Boston (2001), pp. 43–65. · Zbl 0977.16001 |
| [101] | K. I. Beidar and M. A. Chebotar, ”On Lie derivations of Lie ideals of prime algebras,” Israel J. Math., 123, 131–148 (2001). · Zbl 0982.16025 · doi:10.1007/BF02784122 |
| [102] | K. I. Beidar, M. Brešar, M. A. Chebotar, and W. S. Martindale, III, ”On Herstein’s Lie map conjectures. I,” Trans. Amer. Math. Soc., 353, No. 10, 4235–4260 (2001). · Zbl 1019.16019 · doi:10.1090/S0002-9947-01-02731-3 |
| [103] | K. I. Beidar, M. Brešar, M. A. Chebotar, and W. S. Martindale, 3rd, ”On Herstein’s Lie map conjectures. II,” J. Algebra, 238, No. 1, 239–264 (2001). · Zbl 1019.16020 · doi:10.1006/jabr.2000.8628 |
| [104] | K. I. Beidar and B. Torrecillas, ”On actions of Hopf algebras with cocommutative coradical,” J. Pure Appl. Algebra, 161, No. 1–2, 13–30 (2001). · Zbl 0980.16031 · doi:10.1016/S0022-4049(00)00087-6 |
| [105] | K. I. Beidar, M. Brešar, and Y. Fong, ”Extended Jacobson density theorem for Lie ideals of rings with automorphisms,” Publ. Math. Debrecen, 58, No. 3, 325–335 (2001). · Zbl 1004.16029 |
| [106] | K. I. Beidar and M. Brešar, ”Extended Jacobson density theorem for rings with derivations and automorphisms,” Israel J. Math., 122, 317–346 (2001). · Zbl 1003.47029 · doi:10.1007/BF02809906 |
| [107] | K. I. Beidar, Y. Fong, and E. R. Puczy-lowski, ”Polynomial rings over nil rings cannot be homomorphically mapped onto rings with nonzero idempotents,” J. Algebra, 238, No. 1, 389–399 (2001). · Zbl 0996.16015 · doi:10.1006/jabr.2000.8632 |
| [108] | K. I. Beidar, T.-S. Chen, Y. Fong, and W.-F. Ke, ”On graded polynomial identities with an antiautomorphism,” J. Algebra, 256, No. 2, 542–555 (2002). · Zbl 1021.16014 · doi:10.1016/S0021-8693(02)00140-0 |
| [109] | K. I. Beidar, Y. Fong, and W.-F. Ke, ”Maximal right nearring of quotients and semigroup generalized polynomial identity,” Results Math., 42, No. 1–2, 12–27 (2002). · Zbl 1039.16040 |
| [110] | K. I. Beidar, M. Brešar, M. A. Chebotar, and Y. Fong, ”Applying functional identities to some linear preserver problems,” Pacific J. Math., 204, No. 2, 257–271 (2002). · Zbl 1054.46038 · doi:10.2140/pjm.2002.204.257 |
| [111] | K. I. Beidar, Y. Fong, W.-F. Ke, and S. K. Jain, ”An example of a right q-ring,” Israel J. Math., 127, 303–316 (2002). · Zbl 1028.16001 · doi:10.1007/BF02784536 |
| [112] | K. I. Beidar, W.-F. Ke, and E. R. Puczy-lowski, ”On subhereditary radicals and reduced rings,” Proc. Roy. Soc. Edinburgh Sect. A, 132, No. 2, 255–266 (2002). · Zbl 0999.16017 · doi:10.1017/S030821050000161X |
| [113] | K. I. Beidar and W.-F. Ke, ”On essential extensions of direct sums of injective modules,” Arch. Math. (Basel), 78, No. 2, 120–123 (2002). · Zbl 1020.16001 |
| [114] | K. I. Beidar, M. Brešar, M. A. Chebotar, and W. S. Martindale, 3rd, ”On Herstein’s Lie map conjectures. III,” J. Algebra, 249, No. 1, 59–94 (2002). · Zbl 1019.16021 · doi:10.1006/jabr.2001.9076 |
| [115] | K. I. Beidar, M. Brešar, and M. A. Chebotar, ”Functional identities revised: The fractional and the strong degree,” Commun. Algebra, 30, No. 2, 935–969 (2002). · Zbl 1015.16028 · doi:10.1081/AGB-120013192 |
| [116] | K. I. Beidar, W.-F. Ke, and C.-H. Liu, ”On nil subsemigroups of rings with group identities,” Commun. Algebra, 30, No. 1, 347–352 (2002). · Zbl 1044.16018 · doi:10.1081/AGB-120006495 |
| [117] | K. I. Beidar, E. R. Puczy-lowski, and R. Wiegandt, ”Radicals and polynomial rings,” J. Aust. Math. Soc., 72, No. 1, 23–31 (2002). · Zbl 1007.16012 · doi:10.1017/S1446788700003554 |
| [118] | K. I. Beidar, M. V. Zaitsev, and S. A. Pikhtil’kov, ”Lie algebras with the maximality condition for abelian subalgebras,” Vestn. Mosk. Univ. Ser. 1 Mat. Mekh., No. 5, 27–32 (2002). |
| [119] | K. I. Beidar, M. Brešar, and M. A. Chebotar, ”Functional identities with r-independent coefficients,” Commun. Algebra, 30, No. 12, 5725–5755 (2002). · Zbl 1021.16013 · doi:10.1081/AGB-120016007 |
| [120] | K. I. Beidar, M. Brešar, and M. A. Chebotar, ”Jordan superhomomorphisms,” Commun. Algebra, 31, No. 2, 633–644 (2003). · Zbl 1046.16017 · doi:10.1081/AGB-120017336 |
| [121] | K. I. Beidar, W.-F. Ke, C.-H. Liu, and W.-R. Wu, ”Automorphism groups of certain simple 2-(q, 3, {\(\lambda\)}) designs constructed from finite fields,” Finite Fields Appl., 9, No. 4, 401–412 (2003). · Zbl 1032.05011 · doi:10.1016/S1071-5797(03)00013-3 |
| [122] | K. I. Beidar and M. A. Chebotar, ”When is a graded PI algebra a PI algebra?” Commun. Algebra, 31, No. 6, 2951–2964 (2003). · Zbl 1035.16014 · doi:10.1081/AGB-120021901 |
| [123] | K. I. Beidar, S. K. Jain, P. Kanwar, and J. B. Srivastava, ”CS matrix rings over local rings,” J. Algebra, 264, No. 1, 251–261 (2003). · Zbl 1029.16017 · doi:10.1016/S0021-8693(03)00128-5 |
| [124] | K. I. Beidar, M. A. Chebotar, Y. Fong, and W.-F. Ke, ”On certain power-associative, Lie-admissible subalgebras of matrix algebras,” J. Math. Sci., 131, No. 5, 5939–5947 (2005). · Zbl 1160.17318 · doi:10.1007/s10958-005-0452-0 |
| [125] | K. I. Beidar, A. V. Mikhalev, and M. A. Chebotar, ”Functional identities in rings and their applications,” Usp. Mat. Nauk, 59, No. 3(357), 3–30 (2004). · Zbl 1078.16017 |
| [126] | K. I. Beidar and Y.-F. Lin, ”On surjective linear maps preserving commutativity,” Proc. Roy. Soc. Edinburgh Sect. A, 134, No. 6, 1023–1040 (2004). · Zbl 1074.16019 · doi:10.1017/S0308210500003619 |
| [127] | K. I. Beidar, S. K. Jain, and P. Kanwar, ”Nonsingular CS-rings coincide with tight PP rings,” J. Algebra, 282, No. 2, 626–637 (2004). · Zbl 1078.16001 · doi:10.1016/j.jalgebra.2003.12.031 |
| [128] | K. I. Beidar, W.-F. Ke, and E. R. Puczy-lowski, ”On matrix rings and subhereditary radicals,” Commun. Algebra, 32, No. 7, 2827–2839 (2004). · Zbl 1070.16023 · doi:10.1081/AGB-120037418 |
| [129] | K. I. Beidar, K. C. O’Meara, and R. M. Raphael, ”On uniform diagonalisation of matrices over regular rings and one-accessible regular algebras,” Commun. Algebra, 32, No. 9, 3543–3562 (2004). · Zbl 1074.16005 · doi:10.1081/AGB-120039630 |
| [130] | K. I. Beidar, Y. Fong, and E. R. Puczyłowski, ”On essential extensions of reduced rings and domains,” Arch. Math. (Basel), 83, No. 4, 344–352 (2004). · Zbl 1065.16004 |
| [131] | K. I. Beidar, M. Brešar, M. A. Chebotar, and W. S. Martindale, III, ”Polynomial preserving maps on certain Jordan algebras,” Israel J. Math., 141, 285–313 (2004). · Zbl 1060.16026 · doi:10.1007/BF02772225 |
| [132] | K. I. Beidar, S. K. Jain, P. Kanwar, and J. B. Srivastava, ”Semilocal CS matrix rings of order > 1 over group algebras of solvable groups are selfinjective,” J. Algebra, 275, No. 2, 856–858 (2004). · Zbl 1069.16029 · doi:10.1016/j.jalgebra.2003.06.008 |
| [133] | K. I. Beidar and R. Wisbauer, ”On uniform bounds of primeness in matrix rings,” J. Aust. Math. Soc., 76, No. 2, 167–174 (2004). · Zbl 1067.16049 · doi:10.1017/S1446788700008879 |
| [134] | K. I. Beidar and S. K. Jain, ”The structure of right continuous right {\(\pi\)}-rings,” Commun. Algebra, 32, No. 1, 315–332 (2004). · Zbl 1072.16001 · doi:10.1081/AGB-120027869 |
| [135] | K. I. Beidar and S. K. Jain, ”When is every module with essential socle a direct sum of quasi-injectives?” Commun. Algebra, 33, No. 11, 4251–4258 (2005). · Zbl 1119.16004 · doi:10.1080/00927870500279019 |
| [136] | K. I. Beidar and Y.-F. Lin, ”Maps characterized by action on Lie zero products,” Commun. Algebra, 33, No. 8, 2697–2703 (2005). · Zbl 1090.16013 · doi:10.1081/AGB-200064364 |
| [137] | K. I. Beidar, W.-F. Ke, and H. Kiechle, ”Circularity of finite groups without fixed points,” Monatsh. Math., 144, No. 4, 265–273 (2005). · Zbl 1081.20036 · doi:10.1007/s00605-004-0268-x |
| [138] | K. I. Beidar, L. Marki, R. Mlitz, and R. Wiegandt, ”Primitive involution rings,” Acta Math. Acad. Sci. Hungar., 109, No. 4, 357–368 (2005). · Zbl 1094.16020 |
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