RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Journal history Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Fundam. Prikl. Mat.: Year: Volume: Issue: Page: Find

 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 $p$.

Full text: PDF file (223 kB)
References: PDF file   HTML file

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}