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Fundam. Prikl. Mat., 1995, Volume 1, Issue 2, Pages 523–527 (Mi fpm65)  

This article is cited in 2 scientific papers (total in 2 papers)

Short communications

The Nagata–Higman theorem for semirings

A. Ya. Belov

House of scientific and technical work of youth

Abstract: This paper contains the proof of the Nagata–Higman theorem for semirings (with non-commutative addition in general). The main results are the following:
Theorem. Let $A$ be an $l$-generated semiring with commutative addition in which the identity $x^{m}=0$ is satisfied. Then the nilpotency index of $A$ is not greater than $2l^{m+1}m^{3}$.
Nagata–Higman theorem for general semirings. If an $l$-generated semiring satisfies the identity $x^{m}=0$ than every word in it of length greater than $m^{m}\cdot2l^{m+1}m^{3}+ m$ is zero.

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Received: 01.02.1995

Citation: A. Ya. Belov, “The Nagata–Higman theorem for semirings”, Fundam. Prikl. Mat., 1:2 (1995), 523–527

Citation in format AMSBIB
\Bibitem{Bel95}
\by A.~Ya.~Belov
\paper The Nagata--Higman theorem for semirings
\jour Fundam. Prikl. Mat.
\yr 1995
\vol 1
\issue 2
\pages 523--527
\mathnet{http://mi.mathnet.ru/fpm65}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1790979}
\zmath{https://zbmath.org/?q=an:0866.16026}


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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. I. I. Bogdanov, “Examples of nonnilpotent nil-near-rings of nil degree 2”, J. Math. Sci., 128:6 (2005), 3372–3377  mathnet  crossref  mathscinet  zmath
    2. A. Ya. Belov, “Burnside-type problems, theorems on height, and independence”, J. Math. Sci., 156:2 (2009), 219–260  mathnet  crossref  mathscinet  zmath  elib  elib
  • Фундаментальная и прикладная математика
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