π-domains, overrings, and divisorial ideals

Abstract

In this paper we study several generalizations of the concept of unique factorization domain. An integral domain is called a π-domain if every principal ideal is a product of prime ideals. Theorem 1 shows that the class of π-domains forms a rather natural subclass of the class of Krull domains. In Section 3 we consider overrings of π-domains. In Section 4 generalized GCD-domains are introduced: these form an interesting class of domains containing all Prüfer domains and all π-domains.