FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1999, VOLUME 5, NUMBER 1, PAGES 139-147

**On semilocal semigroup rings**

A. V. Zhuchin

Abstract

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The approach for study semilocal semigroup rings over non-radical
rings based on description the structure of semigroup on
the whole is suggested.
The following main statement is proved.
Let $R$ be
a ring, $R$¹ J(R), $S$ be a semigroup with
zero $z$.
The semigroup ring $RS$ is semilocal if and only
if: (i) $R$ is semilocal; (ii) there exists
a chain of ideals $\{z\}=S$_{0} Ì S_{1} Ì ¼ Ì S_{n}=S such
that $S$_{i}/S_{i-1},
$1$£
i £ n, are nil or
completely $0$-simple; (iii) the contracted
semigroup rings $R$_{0}(S_{i}/S_{i-1}),
are semilocal.

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published in Russian.

Location: http://mech.math.msu.su/~fpm/eng/99/991/99110h.htm

Last modified: April 27, 1999