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Fundam. Prikl. Mat., 1995, Volume 1, Issue 4, Pages 1115–1118 (Mi fpm117)  

Short communications

Local semigroup rings

A. Ya. Ovsyannikov

Ural State University

Abstract: The description of local semigroup algebras over a field of characteristic $p$ (if $p>0$, then semigroups are assumed to be locally finite) due to J. Okninsky (1984) is transferred to semigroup rings over non-radical rings. The following statement is proved. Let $R$ be a ring, $R\ne J(R)$, $\operatorname{char}R=0$ ($\operatorname{char}R=p>1$), $S$ be a semigroup (respectively, a locally finite semigroup). The semigroup ring $R[S]$ is local [scalar local] if and only if $R$ is such a ring and $S$ is an ideal extension of a rectangular band (respectively of a completely simple semigroup over a $p$-group) by a locally nilpotent semigroup.

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Bibliographic databases:
UDC: 512.552.7
Received: 01.12.1994

Citation: A. Ya. Ovsyannikov, “Local semigroup rings”, Fundam. Prikl. Mat., 1:4 (1995), 1115–1118

Citation in format AMSBIB
\Bibitem{Ovs95}
\by A.~Ya.~Ovsyannikov
\paper Local semigroup rings
\jour Fundam. Prikl. Mat.
\yr 1995
\vol 1
\issue 4
\pages 1115--1118
\mathnet{http://mi.mathnet.ru/fpm117}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1791797}
\zmath{https://zbmath.org/?q=an:0870.16019}


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