A Note on Locally Inverse Semigroup Algebras

Abstract EN

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/?, 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.