On the endomorphism rings of abelian groups and their Jacobson radical

Victor Bovdi, Alexander Grishkov, Mihail Ursul

Research output: Contribution to journalArticlepeer-review


We give a characterization of those abelian groups which are direct sums of cyclic groups and the Jacobson radicals of their endomorphism rings are closed. A complete characterization of p-groups A for which (EndA, T L) is locally compact, where TL 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 for elementary countable p-groups A.

Original languageEnglish
Pages (from-to)155-165
Number of pages11
JournalPeriodica Mathematica Hungarica
Issue number2
Publication statusPublished - Aug 20 2015


  • Admissible topology
  • Bohr topology
  • Endomorphism ring
  • Finite topology
  • Functorial topology
  • Jacobson radical
  • Liebert topology
  • Quasi-injective module
  • Shift homomorphism
  • Topological ring

ASJC Scopus subject areas

  • General Mathematics


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