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.15682913
Primary Topic
Cancer-related molecular mechanisms research
Type
article
Field-Weighted Citation Impact
0.00
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
article

The Baer-Kaplansky Property of Simple Modules

Zenodo (CERN European Organization for Nuclear Research)
Cancer-related molecular mechanisms research
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)
Reduced inequalities
Openalex Percentile: Top 45%
Cancer-related molecular mechanisms research
DOIOpen Access PDFOpenAlex
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

The Baer-Kaplansky Property of Simple Modules · Zenodo (CERN European Organization for Nuclear Research) (2025) | TGRS Research Map | TGRS