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Fundam. Prikl. Mat., 2008, Volume 14, Issue 8, Pages 55–67 (Mi fpm1189)  

This article is cited in 12 scientific papers (total in 12 papers)

Gröbner–Shirshov bases for Vinberg–Koszul–Gerstenhaber right-symmetric algebras

L. A. Bokutab, Yuqun Chenb, Yu Lib

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b South China Normal University, Guangzhou (Republic of China)

Abstract: In this paper, we establish the composition lemma (diamond lemma) for right-symmetric algebras. As an application, we give a Gröbner–Shirshov basis for the universal enveloping right-symmetric algebra of a Lie algebra.

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English version:
Journal of Mathematical Sciences (New York), 2010, 166:5, 603–612

Bibliographic databases:

UDC: 512.7

Citation: L. A. Bokut, Yuqun Chen, Yu Li, “Gröbner–Shirshov bases for Vinberg–Koszul–Gerstenhaber right-symmetric algebras”, Fundam. Prikl. Mat., 14:8 (2008), 55–67; J. Math. Sci., 166:5 (2010), 603–612

Citation in format AMSBIB
\Bibitem{BokCheLi08}
\by L.~A.~Bokut, Yuqun~Chen, Yu~Li
\paper Gr\"obner--Shirshov bases for Vinberg--Koszul--Gerstenhaber right-symmetric algebras
\jour Fundam. Prikl. Mat.
\yr 2008
\vol 14
\issue 8
\pages 55--67
\mathnet{http://mi.mathnet.ru/fpm1189}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2744933}
\elib{https://elibrary.ru/item.asp?id=12868940}
\transl
\jour J. Math. Sci.
\yr 2010
\vol 166
\issue 5
\pages 603--612
\crossref{https://doi.org/10.1007/s10958-010-9875-3}
\elib{https://elibrary.ru/item.asp?id=15324651}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77952323008}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Bokut L.A., Chen Y., Chen Y., “Gröbner-Shirshov bases for Lie algebras over a commutative algebra”, J. Algebra, 337:1 (2011), 82–102  crossref  mathscinet  zmath  isi  elib
    2. Bokut L.A., Chen Yu., Mo Q., “Grobner-Shirshov Bases for Semirings”, J. Algebra, 385 (2013), 47–63  crossref  mathscinet  zmath  isi  elib
    3. Leonid A. Bokut, Yuqun Chen, “Gröbner–Shirshov bases and PBW theorems”, Zhurn. SFU. Ser. Matem. i fiz., 6:4 (2013), 417–427  mathnet
    4. Bokut L.A., Chen Yu., “Grobner-Shirshov Bases and Their Calculation”, Bull. Math. Sci., 4:3 (2014), 325–395  crossref  mathscinet  zmath  isi  elib
    5. Li Yu., Mo Q., “On Free Pre-Lie Algebras”, Algebr. Colloq., 24:2 (2017), 267–284  crossref  mathscinet  zmath  isi  scopus
    6. Kolesnikov P., “Grobner-Shirshov Bases For Pre-Associative Algebras”, Commun. Algebr., 45:12 (2017), 5283–5296  crossref  mathscinet  zmath  isi  scopus
    7. Li Yu., Mo Q., “Embedding Into 2-Generated Simple Associative (Lie) Algebras”, Commun. Algebr., 45:6 (2017), 2435–2443  crossref  mathscinet  zmath  isi  scopus
    8. Dzhumadil'daev A.S., Ismailov N.A., “Polynomial Identities of Bicommutative Algebras, Lie and Jordan Elements”, Commun. Algebr., 46:12 (2018), 5241–5251  crossref  mathscinet  zmath  isi  scopus
    9. Al-Kaabi M.J.H., Manchon D., Patras F., “Monomial Bases and Pre-Lie Structure For Free Lie Algebras”, J. Lie Theory, 28:4 (2018), 941–967  mathscinet  zmath  isi
    10. Li Yu., Mo Q., Zhao X., “Grobner-Shirshov Bases For Brace Algebras”, Commun. Algebr., 46:11 (2018), 4577–4589  crossref  mathscinet  zmath  isi  scopus
    11. Tuniyaz R. Bokut L.A. Xiryazidin M. Obul A., “Grobner-Shirshov Bases For Free Gelfand-Dorfman-Novokov Algebras and For Right Ideals of Free Right Leibniz Algebras”, Commun. Algebr., 46:10 (2018), 4392–4402  crossref  mathscinet  zmath  isi  scopus
    12. Tuniyaz R., Obul A., “Grobner-Shirshov Basis Method For Multiple Tensor Products of Some Associative Algebras”, Asian-Eur. J. Math., 12:1 (2019), 1950015  crossref  mathscinet  zmath  isi  scopus
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