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International Journal of Mathematics and Mathematical Sciences
Volume 2009, Article ID 349010, 8 pages
Research Article

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

1Dipartimento di Matematica, Università degli Studi “Roma Tre”, 00146 Rome, Italy
2Department of Mathematics, Idaho State University, Pocatello, ID 83209, USA

Received 16 July 2009; Accepted 14 November 2009

Academic Editor: Siamak Yassemi

Copyright © 2009 Marco Fontana and Muhammad Zafrullah. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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