Duals and Transforms of Ideals in PVMDs

Abstract

In this article we study when the dual of a t-ideal in a Prüfer V-Multiplication Domain (PVMD) is a ring and we treat the question of when it coincides with its endomorphism ring. We also study particular classes of overrings of PVMDs. Specifically, we investigate the Nagata transform and the endomorphism ring of ideals in PVMDs in an attempt to establish analogues for well-known results on overrings of Prüfer domains.

Key Words:

• Dual of ideal
• t-ideal
• Ideal transform
• Overring
• PVMD

2000 Mathematics Subject Classification:

• Primary 13A15
• 13A18
• 13F05. Secondary 13G05
• 13F30

ACKNOWLEDGMENT

The authors would like to express their sincere thanks to the referee for his/her helpful suggestions and comments that greatly improved the article.

This work is supported by KFUPM.

Notes

Communicated by I. Swanson.