A “υ-Operation Free” Approach to Prüfer υ-Multiplication Domains

الملخص EN

The so-called Prüfer υ-multiplication domains (PυMDs) are usually defined as domains whose finitely generated nonzero ideals are t-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 the υ-operation and the t-operation.

In this paper, we provide characterizations of and basic results on PυMDs and related notions without star operations.