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 language | English |
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Pages (from-to) | 223-237 |
Number of pages | 15 |
Journal | Applied General Topology |
Volume | 19 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2018 |
Keywords
- Bohr topology
- Endomorphism ring
- Finite topology
- Locally compact ring
- Topological ring
ASJC Scopus subject areas
- Geometry and Topology