On the endomorphism rings of abelian groups and their Jacobson radical

2014/07/05 by V. Bovdi, Victor Bovdi, A. Grishkov +5
Mathematics · #16A65 #16N40 #16S50 #16W80 #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Group Theory (math.GR) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #math.GN #math.GR #math.RA #msc:16A65 #msc:16N40 #msc:16S50 #msc:16W80

paper · pdf · doi:10.48550/arxiv.1407.1362

14 pages

openalex publication_date 2014/07/05 · arxiv created 2014/10/19 · arxiv updated 2014/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a characterization of those abelian groups which are direct sums of cyclic groups and the Jacobson radical of their endomorphism rings are closed. A complete characterization of p-groups A for which (EndA,\mathcal T_L) is locally compact, where \mathcal T_L is the Liebert topology on EndA, is given. We prove that if A is a countable elementary p-group then EndA has a non-admissible ring topology. To every functorial topology on A a right bounded ring topology on EndA is attached. By using this topology we construct on EndA a non-metrizable and non-admissibe ring topology on EndA for elementary countable p-groups A.

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