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 S₁ 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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Last modified: April 27, 1999