Completely simple endomorphism rings of modules




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


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.


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Author Biographies

Victor Bovdi, UAE University

Department of Mathematical Sciences

Mohamed Salim, UAE University

Department of Mathematical Sciences


Mihail Ursul, University of Technology

Department of Mathematics and Computer ScienceProfessor


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How to Cite

V. Bovdi, M. Salim, and M. Ursul, “Completely simple endomorphism rings of modules”, Appl. Gen. Topol., vol. 19, no. 2, pp. 223–237, Oct. 2018.



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