On Dedekind Modules

Abstract

In this article the authors give the relation between a finitely-generated torsionfree Dedekind module M over a domain R and prime submodules of the 𝒪(M)-module M and the ring 𝒪(M). They also prove that M is a finitely-generated torsionfree Dedekind module over a domain R if and only if every semi-maximal submodule of R-module M is invertible.

Key Words:

• Dedekind modules
• Invertible submodules
• Prime submodules
• Pi(π)-module

Mathematics Subject Classification:

• Primary 13C10
• 13F05
• Secondary 13C13

ACKNOWLEDGMENT

Some of this work was carried out during a visit of the second author to Hacettepe University in October 2005. He would like to thank TUBITAK for their financial support.

Notes

Communicated by I. Swanson.