Prüfer v-Multiplication Domains and w-Multiplicative Canonical Ideals

Abstract

Let R be an integral domain. A w-ideal I of R is called a w-multiplicative canonical ideal if (I: (I: J)) = J for each w-ideal J of R. In particular, if R is a w-multiplicative canonical ideal of R, then R is a w-divisorial domain. These are the w-analogues of the concepts of a multiplicative canonical ideal and a divisorial domain, respectively. Motivated by the articles [8, 10], we study the domains possessing w-multiplicative canonical ideals; in particular, we consider Prüfer v-multiplication domains.

Key Words:

• Divisorial ideal
• w-Multiplicative canonical ideal
• Prüfer v-multiplication domain
• Weakly Matlis domain

2000 Mathematics Subject Classification:

• 13A15
• 13F05
• 13G05

ACKNOWLEDGMENTS

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010-0021883).

Notes

Communicated by R. Wiegand.