(FUNDAMENTAL AND APPLIED MATHEMATICS)

2001, VOLUME 7, NUMBER 3, PAGES 939-944

## Local contracted semigroup rings

A. V. Zhuchin

Abstract

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The local contracted semigroup rings $R$0S over non-radical rings $R$ ($\overline R=R/J\left(R\right)\ne \\left\{0\\right\}$) are under consideration. The following main statement is proved. Let $R$ be a ring, $\overline R\ne \\left\{0\\right\}$, $S$ be a semigroup with zero. The ring $R$0S is local if and only if: (i) there exists a nil ideal $N$Í S such that $S/N$@ T0 is a semigroup $T$ (without zero) with adjoint zero; (ii) $RT$ is local, $R$0N is radical.

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