On Invertible and Dense Submodules

Abstract

In this paper, the authors give a partial characterization of invertible, dense and projective submodules. In the final section, they give the equivalent conditions to be invertible, dense and projective submodules for a given an R-module M. They also provide conditions under which a given ring R is a Dedekind domain if and only if every non zero submodule of an R-module is locally free.

Key Words:

• Invertible submodules
• Dense submodules
• Projective submodules
• Locally free submodules
• Dedekind domain

2000 Mathematics Subject Classification:

• 13C10
• 13C13

Acknowledgments

We would like to give our very special thanks to the referee for her/his remarks that have improved the presentation of this paper.

Notes

^#Communicated by I. Swanson.