SOME NOTES ON DEDEKIND MODULES

Year 2011, Volume: 40 Issue: 5, 627 - 634, 01.05.2011

Mehdi Khoramdel Saboura D.p. Hesari

Abstract

SOME NOTES ON DEDEKIND MODULES

Abstract

In this paper, we give the relation between a finitely generated torsion free Dedekind module and the endomorphism ring of O(M)M. In addition it is proved that the endomorphism ring of a finitely generated torsion free Dedekind module M is a Dedekind domain. Also, we give equivalent condition for Dedekind modules, duo modules and uniform modules. Various properties and characterizations of Dedekind modules over integral domains are considered and consequently, necessary and sufficient conditions for an R-module M to be a Dedekind module are given.

Keywords

Dedekind modules and Dedekind domains, Invertible submodules, Duo modules, 2000 AMS Classification: Primary 13 C 10

References

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