Completely simple endomorphism rings of modules

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2 Citations (Scopus)

Abstract

It is proved that if Ap is a countable elementary abelian p-group, then: (i) The ring End(Ap) does not admit a nondiscrete locally compact ring topology. (ii) Under (CH) the simple ring End (Ap)/I, where I is the ideal of End (Ap) consisting of all endomorphisms with finite images, does not admit a nondiscrete locally compact ring topology. (iii) The finite topology on End (Ap) is the only second metrizable ring topology on it. Moreover, a characterization of completely simple endomorphism rings of modules over commutative rings is obtained.

Original languageEnglish
Pages (from-to)223-237
Number of pages15
JournalApplied General Topology
Volume19
Issue number2
DOIs
Publication statusPublished - 2018

Keywords

  • Bohr topology
  • Endomorphism ring
  • Finite topology
  • Locally compact ring
  • Topological ring

ASJC Scopus subject areas

  • Geometry and Topology

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