A Baer-Kaplansky theorem for modules over principal ideal domains

Simion Breaz

A Baer-Kaplansky theorem for modules over principal ideal domains

Commutative Algebra 2014-10-13 v1

Authors: Simion Breaz

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.

Keywords

module theory commutative algebra commutative ring theory

Cite

@article{arxiv.1410.2667,
  title  = {A Baer-Kaplansky theorem for modules over principal ideal domains},
  author = {Simion Breaz},
  journal= {arXiv preprint arXiv:1410.2667},
  year   = {2014}
}

Comments

preprint version; the final version is accepted by JCA

A Baer-Kaplansky theorem for modules over principal ideal domains

Abstract

Keywords

Cite

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