Regular proper *-semigroup embeddings and involutionstitle

Abstract

It is proved that if (S,∗) is a proper *-semigroup and if D is 0-characteristic integral domain then (D[S],∗) is nil-semisimple provided that S is finite or i ∈ D.Let (S,∗) be a finite proper *-semigroup and F be a finite field of characteristic p such that (F[S],∗) is a proper *-ring. Then F[S] is a direct product of fields and 2×2 matrix rings over fields. Furthermore, p≠2,p≠1 mod 4.