A Baer-Kaplansky theorem for modules over principal ideal domains

2014/10/10 by Simion Breaz, Breaz, Simion
Mathematics · Medicine · #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Magnolia and Illicium research #Rings, Modules, and Algebras #math.AC

paper · pdf · doi:10.48550/arxiv.1410.2667

preprint version; the final version is accepted by JCA

arxiv created 2014/10/10 · openalex publication_date 2014/10/10 · arxiv updated 2014/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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⊕ G) and End_R(R⊕ H) are isomorphic then G≅ H. Conversely, if R is a Dedekind domain such that two R-modules G and H are isomorphic whenever the rings End_R(R⊕ G) and End_R(R⊕ H) are isomorphic then R is a PID.

Citations

• Generalizing the Baer-Kaplansky Theorem

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