Completely simple endomorphism rings of modules

Victor Bovdi, Mohamed Salim, Mihail Ursul


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.


topological ring; endomorphism ring; Bohr topology; finite topology; locally compact ring.

Subject classification

16W80; 16N20; 16S50; 16N40.

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