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Fundam. Prikl. Mat., 2006, Volume 12, Issue 2, Pages 101–110 (Mi fpm937)  

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

Combinatorial generators of the multilinear polynomial identities

V. N. Latyshev

M. V. Lomonosov Moscow State University

Abstract: A Gröbner–Shirshov basis (a combinatorial system of generators) is defined in the set of multilinear elements of a T-ideal of the free associative algebra with a countable set of indeterminates. A combinatorial version of the well-known Specht problem about the finite basedness of polynomial identities of an arbitrary associative algebra is formulated. A “combinatorial Spechtness” property of the multilinear product of commutators of degree 2 and the same property for the three-linear commutator are established.

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English version:
Journal of Mathematical Sciences (New York), 2008, 149:2, 1107–1112

Bibliographic databases:

UDC: 512.554

Citation: V. N. Latyshev, “Combinatorial generators of the multilinear polynomial identities”, Fundam. Prikl. Mat., 12:2 (2006), 101–110; J. Math. Sci., 149:2 (2008), 1107–1112

Citation in format AMSBIB
\Bibitem{Lat06}
\by V.~N.~Latyshev
\paper Combinatorial generators of the multilinear polynomial identities
\jour Fundam. Prikl. Mat.
\yr 2006
\vol 12
\issue 2
\pages 101--110
\mathnet{http://mi.mathnet.ru/fpm937}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2249695}
\zmath{https://zbmath.org/?q=an:1163.16013}
\transl
\jour J. Math. Sci.
\yr 2008
\vol 149
\issue 2
\pages 1107--1112
\crossref{https://doi.org/10.1007/s10958-008-0049-5}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-38549084630}


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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. A. Ya. Belov, M. I. Kharitonov, “Subexponential estimates in Shirshov's theorem on height”, Sb. Math., 203:4 (2012), 534–553  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. A. Ya. Belov, M. I. Kharitonov, “Subexponential estimates in the height theorem and estimates on numbers of periodic parts of small periods”, J. Math. Sci., 193:4 (2013), 493–515  mathnet  crossref
    3. V. N. Latyshev, “Finiteness of the standard basis of a $T$-ideal containing Lie nilpotency of index $4$”, J. Math. Sci., 193:4 (2013), 530–536  mathnet  crossref
    4. M. I. Kharitonov, “Otsenki, svyazannye s teoremoi Shirshova o vysote”, Chebyshevskii sb., 15:4 (2014), 55–123  mathnet
    5. V. N. Latyshev, “Finite combinatorial generation of metabelian $T$-ideal”, J. Math. Sci., 233:5 (2018), 702–712  mathnet  crossref
  • Фундаментальная и прикладная математика
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