期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2008
卷号：2008
DOI：10.1155/2008/576061
出版社：Hindawi Publishing Corporation
摘要：Let 𝑅 be a commutative ring and 𝑆 a finite locally inverse semigroup.
It is proved that the semigroup algebra 𝑅[𝑆] is isomorphic to the direct
product of Munn algebras ℳ(𝑅[𝐺𝐽],𝑚𝐽,𝑛𝐽;𝑃𝐽) with
𝐽∈𝑆/𝒥, where
𝑚𝐽 is the number of ℛ-classes in 𝐽, 𝑛𝐽 the number of ℒ-classes in 𝐽, and
𝐺𝐽 a maximum subgroup of 𝐽. As applications, we obtain the sufficient
and necessary conditions for the semigroup algebra of a finite locally
inverse semigroup to be semisimple.
