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Mathematics of the USSR-Sbornik, 1975, Volume 25, Issue 4, Pages 507–523
DOI: https://doi.org/10.1070/SM1975v025n04ABEH002459
(Mi sm3407)
 

This article is cited in 27 scientific papers (total in 28 papers)

Identical relations in finite Lie rings

Yu. A. Bakhturin, A. Yu. Ol'shanskii
References:
Abstract: The article is devoted to proving that the identical relations of a finite Lie ring are consequences of a finite number of such relations. Some of the results on algebraic Lie algebras may be of independent interest.
Bibliography: 13 titles.
Received: 25.06.1974
Bibliographic databases:
UDC: 519.48
MSC: 17B99
Language: English
Original paper language: Russian
Citation: Yu. A. Bakhturin, A. Yu. Ol'shanskii, “Identical relations in finite Lie rings”, Math. USSR-Sb., 25:4 (1975), 507–523
Citation in format AMSBIB
\Bibitem{BakOls75}
\by Yu.~A.~Bakhturin, A.~Yu.~Ol'shanskii
\paper Identical relations in finite Lie rings
\jour Math. USSR-Sb.
\yr 1975
\vol 25
\issue 4
\pages 507--523
\mathnet{http://mi.mathnet.ru/eng/sm3407}
\crossref{https://doi.org/10.1070/SM1975v025n04ABEH002459}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=374219}
\zmath{https://zbmath.org/?q=an:0319.17004}
Linking options:
  • https://www.mathnet.ru/eng/sm3407
  • https://doi.org/10.1070/SM1975v025n04ABEH002459
  • https://www.mathnet.ru/eng/sm/v138/i4/p543
  • This publication is cited in the following 28 articles:
    1. BIN BIN HAN, WEN TING ZHANG, YAN FENG LUO, “FINITE BASIS PROBLEM FOR INVOLUTION MONOIDS OF ORDER FIVE”, Bull. Aust. Math. Soc., 109:2 (2024), 350  crossref
    2. Daniela Martinez Correa, Plamen Koshlukov, “Specht property of varieties of graded Lie algebras”, Monatsh Math, 202:1 (2023), 65  crossref
    3. CLAUDEMIR FIDELIS, PLAMEN KOSHLUKOV, “-graded identities of the Lie algebras in characteristic 2”, Math. Proc. Camb. Phil. Soc., 174:1 (2023), 49  crossref
    4. Edmond W. H. Lee, Frontiers in Mathematics, Advances in the Theory of Varieties of Semigroups, 2023, 1  crossref
    5. Vesselin Drensky, “Weak polynomial identities and their applications”, Communications in Mathematics, 29:2 (2021), 291  crossref
    6. Meng Gao, Wen-Ting Zhang, Yan-Feng Luo, “Finite basis problem for Lee monoids with involution”, Communications in Algebra, 49:10 (2021), 4258  crossref
    7. L. A. Bokut, “Early history of the theory of rings in Novosibirsk”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2017, no. 2, 5–23  mathnet  mathscinet
    8. Edmond W. H. Lee, “Equational theories of unstable involution semigroups”, ERA-MS, 24 (2017), 10  crossref
    9. E.W.. H. Lee, W.T.ing Zhang, “Finite basis problem for semigroups of order six”, LMS J. Comput. Math, 18:01 (2015), 1  crossref  mathscinet
    10. Klyachko A.A., Menshova E.V., “The Identities of Additive Binary Arithmetics”, Electron. J. Comb., 19:1 (2012), P40  crossref  mathscinet  zmath  isi
    11. A. Ya. Belov, “The local finite basis property and local representability of varieties of associative rings”, Izv. Math., 74:1 (2010), 1–126  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    12. Kozik M., “A 2Exptime Complete Varietal Membership Problem”, SIAM J. Comput., 38:6 (2009), 2443–2467  crossref  mathscinet  zmath  isi
    13. D. S. Ananichev, M. V. Volkov, “Varieties of solvable Lie rings of finite width”, Math. Notes, 63:5 (1998), 569–574  mathnet  crossref  crossref  mathscinet  zmath  isi
    14. D. S. Ananichev, “Almost distributive varieties of Lie rings”, Sb. Math., 186:4 (1995), 465–483  mathnet  crossref  mathscinet  zmath  isi
    15. M. V. Zaicev, “Special Lie algebras”, Russian Math. Surveys, 48:6 (1993), 111–152  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    16. Son N., “Identities Satisfied by Finite Representations of Groups in Associative Algebras”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1992, no. 5, 8–12  zmath  isi
    17. V. D. Mazurov, “Solved problems in the Kourovka Notebook”, Russian Math. Surveys, 46:5 (1991), 137–182  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    18. Krasilnikov A., Shmelkin A., “On Finite Bases for Laws of Triangular Matrices”, Lect. Notes Math., 1456 (1990), 12–13  mathscinet  isi
    19. A. A. Premet, K. N. Semenov, “Varieties of residually finite Lie algebras”, Math. USSR-Sb., 65:1 (1990), 109–118  mathnet  crossref  mathscinet  zmath
    20. Skiba A., “Subformation of Varieties of Algebraic Systems”, Dokl. Akad. Nauk Belarusi, 30:1 (1986), 9–12  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    References:91
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