The Baer-Kaplansky Property of Simple Modules

In this paper we study the Baer-Kaplansky property of simple modules. We show that if R=F[x], where F is a subfield of an algebraically closed field C with 1 < [C:F]<infty, and B is a Baer-Kaplansky class of simple R-modules, then |B|\leq 2. We also show that over many algebras (both hereditary and non-hereditary) and over many matrix rings (which are not algebras) the class of simple modules is not a Baer-Kaplansky class.

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2025-05-15
DOI
https://doi.org/10.5281/zenodo.15682914
Primary Topic
Advanced Electron Microscopy Techniques and Applications
Type
article
Field-Weighted Citation Impact
0.00
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article

The Baer-Kaplansky Property of Simple Modules

Zenodo (CERN European Organization for Nuclear Research)
Advanced Electron Microscopy Techniques and Applications
article

The Baer-Kaplansky Property of Simple Modules

article en

Abstract

In this paper we study the Baer-Kaplansky property of simple modules. We show that if R=F[x], where F is a subfield of an algebraically closed field C with 1 < [C:F]<infty, and B is a Baer-Kaplansky class of simple R-modules, then |B|\leq 2. We also show that over many algebras (both hereditary and non-hereditary) and over many matrix rings (which are not algebras) the class of simple modules is not a Baer-Kaplansky class.

Zenodo (CERN European Organization for Nuclear Research)
Openalex Percentile: Top 71%
Advanced Electron Microscopy Techniques and Applications
DOIOpen Access PDFOpenAlex
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The Baer-Kaplansky Property of Simple Modules · Zenodo (CERN European Organization for Nuclear Research) (2025) | TGRS Research Map | TGRS