International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 576061, 5 pages
doi:10.1155/2008/576061

A note on locally inverse semigroup algebras.

Abstract

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.