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

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Location: http://mech.math.msu.su/~fpm/eng/k01/k013/k01324h.htm

Last modified: December 23, 2001