FPM 2001, vol. 7, no. 3, pp. 939-944

FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(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 $N$ 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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