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Mat. Sb. (N.S.), 1975, Volume 96(138), Number 4, Pages 543–559 (Mi msb3407)  

This article is cited in 19 scientific papers (total in 20 papers)

Identical relations in finite Lie rings

Yu. A. Bakhturin, A. Yu. Ol'shanskii


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.

Full text: PDF file (2070 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1975, 25:4, 507–523

Bibliographic databases:

UDC: 519.48
MSC: 17B99
Received: 25.06.1974

Citation: Yu. A. Bakhturin, A. Yu. Ol'shanskii, “Identical relations in finite Lie rings”, Mat. Sb. (N.S.), 96(138):4 (1975), 543–559; 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 Mat. Sb. (N.S.)
\yr 1975
\vol 96(138)
\issue 4
\pages 543--559
\mathnet{http://mi.mathnet.ru/msb3407}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=374219}
\zmath{https://zbmath.org/?q=an:0319.17004}
\transl
\jour Math. USSR-Sb.
\yr 1975
\vol 25
\issue 4
\pages 507--523
\crossref{https://doi.org/10.1070/SM1975v025n04ABEH002459}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Yu. A. Bahturin, A. Yu. Ol'shanskii, “Solvable just-non-Cross varieties of Lie rings”, Math. USSR-Sb., 29:3 (1976), 345–358  mathnet  crossref  mathscinet  zmath  isi
    2. Yu. L. Ershov, Yu. I. Merzlyakov, “Chetyrnadtsataya Vsesoyuznaya algebraicheskaya konferentsiya”, UMN, 33:1(199) (1978), 239–244  mathnet
    3. V. A. Artamonov, “Lattices of varieties of linear algebras”, Russian Math. Surveys, 33:2 (1978), 155–193  mathnet  crossref  mathscinet  zmath
    4. G. V. Sheina, “Metabelian varieties of Lie $A$-algebras”, Russian Math. Surveys, 33:2 (1978), 249–250  mathnet  crossref  mathscinet  zmath
    5. Yu. A. Medvedev, “Cross varieties of algebras”, Math. USSR-Sb., 43:3 (1982), 347–376  mathnet  crossref  mathscinet  zmath
    6. M. V. Volkov, A. G. Gein, “Identities in almost nilpotent Lie rings”, Math. USSR-Sb., 46:1 (1983), 133–142  mathnet  crossref  mathscinet  zmath
    7. Trahtman A., “The Finite Basis Question for Semigroups of Order Less Than 6”, Semigr. Forum, 27:1-4 (1983), 387–389  crossref  mathscinet  zmath  isi
    8. Skiba A., “Subformation of Varieties of Algebraic Systems”, Dokl. Akad. Nauk Belarusi, 30:1 (1986), 9–12  mathscinet  zmath  isi
    9. A. A. Premet, K. N. Semenov, “Varieties of residually finite Lie algebras”, Math. USSR-Sb., 65:1 (1990), 109–118  mathnet  crossref  mathscinet  zmath
    10. Krasilnikov A., Shmelkin A., “On Finite Bases for Laws of Triangular Matrices”, Lect. Notes Math., 1456 (1990), 12–13  mathscinet  isi
    11. V. D. Mazurov, “Solved problems in the Kourovka Notebook”, Russian Math. Surveys, 46:5 (1991), 137–182  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    12. 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
    13. M. V. Zaicev, “Special Lie algebras”, Russian Math. Surveys, 48:6 (1993), 111–152  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    14. D. S. Ananichev, “Almost distributive varieties of Lie rings”, Sb. Math., 186:4 (1995), 465–483  mathnet  crossref  mathscinet  zmath  isi
    15. 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
    16. Kozik M., “A 2Exptime Complete Varietal Membership Problem”, SIAM J. Comput., 38:6 (2009), 2443–2467  crossref  mathscinet  zmath  isi
    17. 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
    18. Klyachko A.A., Menshova E.V., “The Identities of Additive Binary Arithmetics”, Electron. J. Comb., 19:1 (2012), P40  crossref  mathscinet  zmath  isi
    19. 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
    20. 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
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