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J. Sib. Fed. Univ. Math. Phys., 2013, Volume 6, Issue 4, Pages 417–427 (Mi jsfu327)  

This article is cited in 5 scientific papers (total in 5 papers)

Gröbner–Shirshov bases and PBW theorems

Leonid A. Bokutab, Yuqun Chenb

a Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia
b School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, P. R. China

Abstract: We review some applications of Gröbner–Shirshov bases, including PBW theorems, linear bases of free universal algebras, normal forms for groups and semigroups, extensions of groups and algebras, embedding of algebras.

Keywords: Gröbner–Shirshov basis, Composition-Diamond lemma, PBW theorem, normal form, group, semigroup, extension.

Full text: PDF file (179 kB)
References: PDF file   HTML file
UDC: 512.5
Received: 18.09.2013
Received in revised form: 02.10.2013
Accepted: 04.11.2013
Language:

Citation: Leonid A. Bokut, Yuqun Chen, “Gröbner–Shirshov bases and PBW theorems”, J. Sib. Fed. Univ. Math. Phys., 6:4 (2013), 417–427

Citation in format AMSBIB
\Bibitem{BokChe13}
\by Leonid~A.~Bokut, Yuqun~Chen
\paper Gr\"obner--Shirshov bases and PBW theorems
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2013
\vol 6
\issue 4
\pages 417--427
\mathnet{http://mi.mathnet.ru/jsfu327}


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    This publication is cited in the following articles:
    1. Yu. Li, Q. Mo, “On free pre-Lie algebras”, Algebr. Colloq., 24:2 (2017), 267–284  crossref  mathscinet  zmath  isi  scopus
    2. P. Kolesnikov, “Gröbner-Shirshov bases for pre-associative algebras”, Commun. Algebr., 45:12 (2017), 5283–5296  crossref  mathscinet  zmath  isi  scopus
    3. Y. Li, Q. H. Mo, “Some new results for Leibniz algebras and non-associative algebras”, Southeast Asian Bull. Math., 41:1 (2017), 45–54  mathscinet  isi
    4. I. Ivanov-Pogodaev, S. Malev, “Finite Gröbner basis algebras with unsolvable nilpotency problem and zero divisors problem”, J. Algebra, 508 (2018), 575–588  crossref  mathscinet  zmath  isi  scopus
    5. Kanel-Belov A., Chilikov A., Ivanov-Pogodaev I., Malev S., Plotkin E., Yu J.-T., Zhang W., “Nonstandard Analysis, Deformation Quantization and Some Logical Aspects of (Non)Commutative Algebraic Geometry”, Mathematics, 8:10 (2020), 1694  crossref  isi  scopus
  • Журнал Сибирского федерального университета. Серия "Математика и физика"
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