International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 349010, 8 pages
doi:10.1155/2009/349010
A “υ-Operation Free” Approach to Prüfer υ-Multiplication Domains
Marco Fontana1
and Muhammad Zafrullah2
1Dipartimento di Matematica, Università degli Studi “Roma Tre”, 00146 Rome, Italy
2Department of Mathematics, Idaho State University, Pocatello, ID 83209, USA
Abstract
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.