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Fundam. Prikl. Mat., 2014, Volume 19, Issue 2, Pages 187–206 (Mi fpm1583)  

Varieties of associative rings containing a finite ring that is nonrepresentable by a matrix ring over a commutative ring

A. Mekei

Mongolian State University, Ulaanbaatar, Mongolia

Abstract: In this paper, we give examples of infinite series of finite rings $B_v^{(m)}$, where $m\geq2$, $0\leq v\leq p-1$, and $p$ is a prime number, that are not representable by matrix rings over commutative rings, and we describe the basis of polynomial identities of these rings. We prove here that every variety $\operatorname{var}B_v^{(m)}$, where $m=2$, or $m-1=(p-1)k$, $k\geq1$, and $p\geq3$, or $p=2$, $m\geq3$, $0\leq v<p$, and $p$ is a prime number, is a minimal variety containing a finite ring that is nonrepresentable by a matrix ring over a commutative ring. Therefore, we describe almost finitely representable varieties of rings whose generating ring contains an idempotent element of additive order $p$.

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English version:
Journal of Mathematical Sciences (New York), 2016, 213:2, 254–267

Bibliographic databases:

UDC: 512.552

Citation: A. Mekei, “Varieties of associative rings containing a finite ring that is nonrepresentable by a matrix ring over a commutative ring”, Fundam. Prikl. Mat., 19:2 (2014), 187–206; J. Math. Sci., 213:2 (2016), 254–267

Citation in format AMSBIB
\Bibitem{Mek14}
\by A.~Mekei
\paper Varieties of associative rings containing a~finite ring that is nonrepresentable by a~matrix ring over a~commutative ring
\jour Fundam. Prikl. Mat.
\yr 2014
\vol 19
\issue 2
\pages 187--206
\mathnet{http://mi.mathnet.ru/fpm1583}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3431921}
\transl
\jour J. Math. Sci.
\yr 2016
\vol 213
\issue 2
\pages 254--267
\crossref{https://doi.org/10.1007/s10958-016-2714-4}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84954527755}


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  • Фундаментальная и прикладная математика
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