On self-injective semigroup rings (Q790259)

Let K be a field and S a semigroup. It is shown that if the semigroup ring K[S] is right self-injective, then K[S] is right perfect. This, in view of a characterization of perfect semigroup rings obtained by the author [Proc. Am. Math. Soc. 89, 49-51 (1983; Zbl 0531.20039)] yields many informations on the structure of S. Further it is proved that for regular semigroups K[S] right self-injective implies S finite. This allows to describe unitary right self-injective rings K[S] of regular semigroups by means of the properties of the semigroup S.