A" υ-Operation Free" Approach to Pr¨ ufer υ-Multiplication Domains

The so-called Prüferυ-multiplication domains (PυMDs) are usually defined as domains whose finitely generated nonzero ideals aret-invertible. These domains generalize Prüfer domains and Krull domains. The PυMDs are relatively obscure compared to their very well-known special cases. One of the reasons could be that the study of PυMDs uses the jargon of star operations, such as theυ-operation and thet-operation. In this paper, we provide characterizations of and basic results on PυMDs and related notions without star operations.