(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 $R$ ($\overline R=R/J(R)\ne\{0\}$) are under consideration. The following main statement is proved. Let $R$ be a ring, $\overline R\ne\{0\}$, $S$ be a semigroup with zero. The ring $R_0S$ is local if and only if: (i) there exists a nil ideal $N\subseteq S$ such that $S/N\cong T^0$ is a semigroup $T$ (without zero) with adjoint zero; (ii) $RT$ is local, $R_0N$ is radical. 

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Location: http://mech.math.msu.su/~fpm/eng/k01/k013/k01324t.htm.