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Fundam. Prikl. Mat., 2012, Volume 17, Issue 5, Pages 75–85 (Mi fpm1435)  

This article is cited in 1 scientific paper (total in 1 paper)

Finiteness of the standard basis of a $T$-ideal containing Lie nilpotency of index $4$

V. N. Latyshev

M. V. Lomonosov Moscow State University

Abstract: Recently the author presented a notion of standard basis for a $T$-ideal of the free associative algebra over a field of zero characteristic. It was proved that it is finite if the $T$-ideal contains either Lie nilpotency of index $3$ or a multilinear product of commutators of degree $2$. Here we prove the finiteness of the reduced standard basis of any $T$-ideal containing Lie nilpotency of index $4$.

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English version:
Journal of Mathematical Sciences (New York), 2013, 193:4, 530–536

UDC: 512.554

Citation: V. N. Latyshev, “Finiteness of the standard basis of a $T$-ideal containing Lie nilpotency of index $4$”, Fundam. Prikl. Mat., 17:5 (2012), 75–85; J. Math. Sci., 193:4 (2013), 530–536

Citation in format AMSBIB
\Bibitem{Lat12}
\by V.~N.~Latyshev
\paper Finiteness of the standard basis of a~$T$-ideal containing Lie nilpotency of index~$4$
\jour Fundam. Prikl. Mat.
\yr 2012
\vol 17
\issue 5
\pages 75--85
\mathnet{http://mi.mathnet.ru/fpm1435}
\transl
\jour J. Math. Sci.
\yr 2013
\vol 193
\issue 4
\pages 530--536
\crossref{https://doi.org/10.1007/s10958-013-1480-9}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84899437978}


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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. 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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