Semiprimitivity of Orthodox Semigroup Algebras.

LetSbe a finite orthodox semigroup or an orthodox semigroup where the idempotent bandE(S) is locally pseudofinite. In this paper, by using principal factors and Rukolaǐne idempotents, we show that the contracted semigroup algebraR0[S] is semiprimitive if and only ifSis an inverse semigroup andR[G] is semiprimitive for each maximal subgroupGofS. This theorem strengthens previous results about the semiprimitivity of inverse semigroup algebras. [ABSTRACT FROM AUTHOR]