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arXiv · 1410.2667

A Baer-Kaplansky theorem for modules over principal ideal domains

Simion Breaz
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Abstract

We will prove that if $G$ and $H$ are modules over a principal ideal domain $R$ such that the endomorphism rings $\mathrm{End}_R(R\oplus G)$ and $\mathrm{End}_R(R\oplus H)$ 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 $\mathrm{End}_R(R\oplus G)$ and $\mathrm{End}_R(R\oplus H)$ are isomorphic then $R$ is a PID.

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Simion Breaz. 2014-10-10. A Baer-Kaplansky theorem for modules over principal ideal domains. https://arxiv.org/abs/1410.2667

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