Clifford Regular Domains,

The class semigroup of a commutative integral domain R is the semigroup (R) of the isomorphism classes of the nonzero ideals of R with operation induced by multiplication. A domain R is said to be Clifford regular if (R) is a Clifford semigroup, i.e. (R) is the disjoint union of the subgroups associated to the idempotent elements. In this paper we characterize the noetherian and the integrally closed Clifford regular domains and find some properties of an arbitrary Clifford regular domain.