Self-injective semigroup rings for finite inverse semigroups
Ronald H. Wenger · Proceedings of the American Mathematical Society · 1969
The purpose of this article is the proof of the following theorem.F will always denote a ring with identity, and R(S) the semigroup ring (contracted if 5 has a zero) of a semigroup S over R.Theorem.Let S be a finite inverse semigroup.Then R(S) is selfinjective (s.i.) if, and only if, R is s.i.This is an extension of Theorem 8.3 in [3], of part 1 of Theorem 4.1 in [2], and of the corollary to Theorem 1 in [4].The results in [2] and [3 ] are used in its proof.As F has an identity, 5 is assumed embedded in R(S).|X| will denote the cardinality of the set X and X\F will denote the complement of a set F in a set X. Terminology and definitions are given in [l].