SOME NOTES ON DEDEKIND MODULES

Authors : Mehdi KHORAMDEL, Saboura D.p. HESARİ

Pages : 627-634

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Publication Date : 2011-05-01

Article Type : Research Paper

Abstract :In this paper, we give the relation between a finitely generated torsion free Dedekind module and the endomorphism ring of Oinsert ignore into journalissuearticles values(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