SOME CHARACTERIZATIONS OF DEDEKIND MODULES

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Published: Feb 15, 2017
DOI: https://doi.org/10.14403/jcms.2017.30.1.53
Keywords:
Dedekind module, discrete valuation module, cyclic submodule module, factorable module, multiplication module
Mathematics Subject Classification (2020):
Primary 13A15, 13C13

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Tae In Kwon
Department of Applied Mathematics, Changwon National University
Hwankoo Kim
School of Computer and Information Engineering, Hoseo University
Myeong Og Kim
Department of Mathematics, Kyungpook National University

Abstract





In this article, we generalize the concepts of several classes of domains (which are related to a Dedekind domain) to a torsion-free module and it is shown that for a faithful multiplication module over an integral domain, we characterize Dedekind modules, cyclic submodule modules, and discrete valuation modules in terms of factorable modules and a sort of Euclidean algorithm.





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Article Details

Issue
Vol. 30 No. 1 (2017)
Section
Articles