文章基本信息

标题：A Note on Locally Inverse Semigroup Algebras
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作者：Xiaojiang Guo
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.