SOME NOTES ON DEDEKIND MODULES

In this paper, we give the relation between a finitely generated torsion free Dedekind module and the endomorphism ring of O(M)M. In ad- dition 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 mod- ules over integral domains are considered and consequently, necessary and sufficient conditions for an R-module M to be a Dedekind module are given.