Ample semigroups and Frobenius algebras. (Q896252)

Contracted semigroup algebras \(K_0[S]\) of ample semigroups \(S\) over a field \(K\) are considered. It is shown that, if \(K_0[S]\) is right self-injective then \(S\) must be a finite inverse semigroup. Hence, this algebra is also left self-injective and it is a Frobenius algebra. Recall that a semigroup is inverse if and only if it is ample and regular. The proof is based on showing that \(S\) has a finite ideal chain with factors that are weak Brandt semigroups with finitely many idempotents and next that every factor of this chain is actually a finite regular semigroup.