FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

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

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,
$\overline R=R/J(R)\ne 0$ , $S$
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 $\{z\}=S_0\subset S_1\subset\ldots\subset S_n=S$
such that $S_i/S_{i-1}$ , $1\le i\le n$ , are nil or
completely $0$ -simple; $(iii)$ the contracted semigroup
rings $R_0(S_i/S_{i-1})$ , are semilocal.

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Last modified: April 27, 1999