Idempotent elements of class semigroup of prufer domain of finite character

چکیده مقاله

The class semigroup of a commutative integral domain R is the semigroup S(R) of the iso- morphism class of the nonzero ideals of R with operation induced by multiplication. We consider prufer domains of finite character,i.e. Prufer domains in which every nonzero ideal is contained but in a finite number of maximal ideals. In [3] it is proved that, if R is such a prufer domain, then S(R) is the disjoint union of the subgroups associated to each idempotent elements of S(R). In order to understand the structure of S(R), one has to know the idempotent elements of S(R) and the constituent groups associated to them. In this paper we give a description of the idempotent elements of S(R).They are two types. They are represented either by fractional overrings of R or by products of nonzero idempotent prime ideals of R and fractional overrings of R.