一般化された逆半群における特殊対合について

A unary operation * : S→S on a semigroup S is called a special involution if it satisfies (1) (x^*)^*=x, (2) (xy)^*=y^*x^* and (3) xx^*x=x for all x, y∈S. It has been shown by [5] that every special involution in a regular semigroup S is determined by the p-system in S. In this paper, we shall determine all the p-systems in a generalized inverse semigroup S, and accordiugly all the special involutions in S. Further, we shall investigate the cardinality of the set of p-systems in S.