基本正則[*]半群について

Abstract

A semigroup S is called to be fundameutal if its only one comgruence contaiued in the Green's relation 〓 on S is the trivial one. Let S be a regular * semigroup, and let E and P be the sets of idempotents and projections of S, respectively. In his paper [3], T. E. Hall gives us the construction of a fundamental regular semigroup T_<E> which is a generalization of [2] and [4]. In this paper, we shall show that the set of projections plays an important role in the theory of regular * semigroups, and construct a fundamental regular * semigroup T_p, say, by using P instead of <E>.