Uniform Quasi-Dedekind Modules

Adil G. Naoum, Ali S. Mijbass


Let R be a commutative ring with 1, and M is a unitary R-module. A submodule N of M is called quasi-invertible if Hom(M/N, M)=0,and M is said to be quasi-Dedekind module if every non-zero submodule of M is quasi-invertible. In this paper, we continue the study of quasi-Dedekind modules that was started by the authors.
In particular, we prove that the ring of endomorphisms of a uniform quasi-Dedekind module is an integral domain. We also study quasi-Dedekind modules over Dedekind ring, we prove, among other things, that the only quasi-Dedekind dualizable Z-module is Z. The main result of the paper shows that every uniform faithful quasi-Dedekind R-module is isomorphic to a submodule of Q(R).


Dedekind domain, quasi-Dedekind module, ring of endomorphisms, dualizable module, field of quotient

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