STRUCTURE OF GENERAL IDEAL SEMIGROUPS OF MONOIDS AND DOMAINS

Let H be a monoid (respectively, an integral domain) and r an ideal system on H. In this paper we investigate the r-ideal semigroup of H. One goal is to specify monoids such that their r-ideal semigroup possesses semigroup-theoretical properties, like almost completeness, pi-regularity and completeness. Moreover, if H is an integral domain and * a star operation on H, then we provide conditions on H such that the idempotents of the *-ideal semigroup are trivial or such that H is pi*-stable.