FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2001, VOLUME 7, NUMBER 3, PAGES 939-944
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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Last modified: December 23, 2001