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Mat. Sb. (N.S.), 1958, Volume 45(87), Number 2, Pages 113–122 (Mi msb4963)  

This article is cited in 31 scientific papers (total in 31 papers)

On free Lie rings

A. I. Shirshov


Full text: PDF file (1022 kB)

Bibliographic databases:
Received: 30.11.1956

Citation: A. I. Shirshov, “On free Lie rings”, Mat. Sb. (N.S.), 45(87):2 (1958), 113–122

Citation in format AMSBIB
\Bibitem{Shi58}
\by A.~I.~Shirshov
\paper On free Lie rings
\jour Mat. Sb. (N.S.)
\yr 1958
\vol 45(87)
\issue 2
\pages 113--122
\mathnet{http://mi.mathnet.ru/msb4963}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=99356}
\zmath{https://zbmath.org/?q=an:0080.25503}


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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. L. A. Bokut', “Unsolvability of the equality problem and subalgebras of finitely presented Lie algebras”, Math. USSR-Izv., 6:6 (1972), 1153–1199  mathnet  crossref  mathscinet  zmath
    2. G. P. Kykin, “On free products of restricted Lie algebras”, Math. USSR-Sb., 24:1 (1974), 49–78  mathnet  crossref  mathscinet  zmath
    3. Yu. A. Bakhturin, A. Yu. Ol'shanskii, “Identical relations in finite Lie rings”, Math. USSR-Sb., 25:4 (1975), 507–523  mathnet  crossref  mathscinet  zmath
    4. E. I. Khukhro, “On the associated Lie ring of a free 2-generator group of prime exponent and the Hughes conjecture for 2-generator $p$-groups”, Math. USSR-Sb., 46:4 (1983), 571–579  mathnet  crossref  mathscinet  zmath
    5. Yu. V. Billing, “Affine modular Lie algebras”, Math. USSR-Sb., 70:2 (1991), 573–586  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. A. A. Mikhalev, “Embedding of Lie superalgebras of countable rank in Lie superalgebras with two generators”, Russian Math. Surveys, 45:6 (1990), 162–163  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. Mikhalev A., Zolotykh A., “Standard Grobner-Shirshov Bases of Free Algebras Over Rings, I. Free Associative Algebras”, Int. J. Algebr. Comput., 8:6 (1998), 689–726  crossref  isi
    8. A. V. Gavrilov, “A free associative algebra as a free module over a Specht subalgebra”, Siberian Math. J., 44:3 (2003), 428–434  mathnet  crossref  mathscinet  zmath  isi
    9. N. I. Sandu, “Infinite Independent Systems of Identities of an Associative Algebra over an Infinite Field of Characteristic Two”, Math. Notes, 74:4 (2003), 569–577  mathnet  crossref  crossref  mathscinet  zmath  isi
    10. I. V. Chirkov, M. A. Shevelin, “Zero divisors in amalgamated free products of Lie algebras”, Siberian Math. J., 45:1 (2004), 188–195  mathnet  crossref  mathscinet  zmath  isi  elib
    11. Ufer S., “Pbw Bases for a Class of Braided Hopf Algebras”, J. Algebra, 280:1 (2004), 84–119  crossref  isi
    12. A. N. Koryukin, “Gröbner–Shirshov Bases for the Lie Algebra”, Algebra and Logic, 44:2 (2005), 73–81  mathnet  crossref  mathscinet  zmath  elib  elib
    13. E. S. Chibrikov, “The Right-Normed Basis for a Free Lie Superalgebra and Lyndon–Shirshov Words”, Algebra and Logic, 45:4 (2006), 261–276  mathnet  crossref  mathscinet  zmath  elib
    14. A. N. Koryukin, K.-P. Shum, “Redutsirovannye bazisy algebry Li $D_n^+$”, Sib. zhurn. industr. matem., 9:4 (2006), 90–104  mathnet  mathscinet
    15. Bokut L. Chibrikov E., “Lyndon-Shirshov Words, Grobner-Shirshov Bases, and Free Lie Algebras”, Non-Associative Algebra and its Applications, Monographs and Textbooks in Pure and Applied Mathematics, 246, ed. Sabinin L. Sbitneva L. Shestakov I., Chapman & Hall/Crc Press, 2006, 17–39  isi
    16. Shestakov I. Zhukavets N., “The Free Alternative Superalgebra on One Odd Generator”, Int. J. Algebr. Comput., 17:5-6 (2007), 1215–1247  crossref  isi
    17. A. N. Koryukin, “Gröbner–Shirshov bases of the Lie algebra $B_n^+$”, St. Petersburg Math. J., 20:1 (2009), 65–94  mathnet  crossref  mathscinet  zmath  isi  elib
    18. L. A. Bokut, Yuqun Chen, Yu Li, “Gröbner–Shirshov bases for Vinberg–Koszul–Gerstenhaber right-symmetric algebras”, J. Math. Sci., 166:5 (2010), 603–612  mathnet  crossref  mathscinet  elib  elib
    19. A. N. Koryukin, “Gröbner–Shirshov bases of the Lie algebra $D^+_n$”, St. Petersburg Math. J., 22:4 (2011), 573–614  mathnet  crossref  mathscinet  zmath  isi
    20. E. N. Poroshenko, “Bases for partially commutative Lie algebras”, Algebra and Logic, 50:5 (2011), 405–417  mathnet  crossref  mathscinet  zmath  isi
    21. Koryukin A.N., “Sistemy kornei, redutsirovannye slova i polnye redutsirovannye sistemy sootnoshenii algebr li”, Doklady Akademii nauk vysshei shkoly Rossiiskoi Federatsii, 2011, no. 2, 15–24  elib
    22. E. N. Poroshenko, “Centralizers in partially commutative Lie algebras”, Algebra and Logic, 51:4 (2012), 351–371  mathnet  crossref  mathscinet  zmath  isi
    23. Shved E.A., “O kategorii pronilpotentnykh algebr li”, Vestnik omskogo universiteta, 2012, no. 2, 67–75  elib
    24. M. I. Kharitonov, “Otsenki, svyazannye s teoremoi Shirshova o vysote”, Chebyshevskii sb., 15:4 (2014), 55–123  mathnet
    25. V. Yu. Gubarev, “Free Lie Rota–Baxter algebras”, Siberian Math. J., 57:5 (2016), 809–818  mathnet  crossref  crossref  isi  elib  elib
    26. E. N. Poroshenko, “Universal equivalence of partially commutative Lie algebras”, Algebra and Logic, 56:2 (2017), 133–148  mathnet  crossref  crossref  isi
    27. S. V. Pchelintsev, I. P. Shestakov, “Constants of partial derivations and primitive operations”, Algebra and Logic, 56:3 (2017), 210–231  mathnet  crossref  crossref  isi
    28. Yu. Chen, Y. Li, Q. Tang, “Gröbner–Shirshov bases for some Lie algebras”, Siberian Math. J., 58:1 (2017), 176–182  mathnet  crossref  crossref  isi  elib  elib
    29. V. Yu. Gubarev, “Universalnye obertyvayuschie lievy algebry Roty–Bakstera prelievykh i postlievykh algeb”, Algebra i logika, 58:1 (2019), 3–21  mathnet  crossref
    30. A. Naurazbekova, “On the structure of free dual Leibniz algebras”, Eurasian Math. J., 10:3 (2019), 40–47  mathnet  crossref
    31. Pchelintsev S.V., “Relatively Free Associative Lie Nilpotent Algebras of Rank 3”, Sib. Electron. Math. Rep., 16 (2019), 1937–1946  crossref  isi
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