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SPRING 2015 A Baer-Kaplansky theorem for modules over principal ideal domains
Simion Breaz
J. Commut. Algebra 7(1): 1-7 (SPRING 2015). DOI: 10.1216/JCA-2015-7-1-1

Abstract

We will prove that if $G$ and $H$ are modules over a principal ideal domain $R$ such that the endomorphism rings $\End_R(R\oplus G)$ and $\End_R(R\oplus H)$ are isomorphic, then $G\cong H$. Conversely, if $R$ is a Dedekind domain such that two $R$-modules $G$ and $H$ are isomorphic whenever the rings $\End_R(R\oplus G)$ and $\End_R(R\oplus H)$ are isomorphic, then $R$ is a PID.

Citation

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Simion Breaz. "A Baer-Kaplansky theorem for modules over principal ideal domains." J. Commut. Algebra 7 (1) 1 - 7, SPRING 2015. https://doi.org/10.1216/JCA-2015-7-1-1

Information

Published: SPRING 2015
First available in Project Euclid: 2 March 2015

zbMATH: 1314.13038
MathSciNet: MR3316982
Digital Object Identifier: 10.1216/JCA-2015-7-1-1

Subjects:
Primary: 13G05, 16D70, 16S50, 20K30

Rights: Copyright © 2015 Rocky Mountain Mathematics Consortium

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Vol.7 • No. 1 • SPRING 2015
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