Completely simple endomorphism rings of modules
Rings and Algebras
2017-12-27 v1 General Topology
Abstract
It is proved that if A_p is a countable elementary abelian p-group, then: (i) The ring End(A_p) does not admit a nondiscrete locally compact ring topology. (ii) Under (CH) the simple ring End(A_p)/I, where I is the ideal of End(A_p) consisting of all endomorphisms with finite images, does not admit a nondiscrete locally compact ring topology. (iii) The finite topology on End(A_p) is the only second metrizable ring topology on it. Moreover, a characterization of completely simple endomorphism rings of the endomorphism rings of modules over commutative rings is also obtained.
Cite
@article{arxiv.1712.09186,
title = {Completely simple endomorphism rings of modules},
author = {V. A. Bovdi and M. A. Salim and Mihail Ursul},
journal= {arXiv preprint arXiv:1712.09186},
year = {2017}
}
Comments
16 pages