Completely simple endomorphism rings of modules

Applied General Topology

Victor Bovdi¹  Mohamed Salim¹  Mihail Ursul² 

[1] UAE University;University of Technology

关键词: topological ring;    endomorphism ring;    Bohr topology;    finite topology;    locally compact ring.;   

DOI  :  10.4995/agt.2018.7955

学科分类：几何与拓扑

来源: Open Journal Systems

【 摘 要 】

It is proved that if A pis 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 modules over commutative rings is obtained.

【 授权许可】

CC BY-NC-ND