Completely simple endomorphism rings of modules
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 the endomorphism rings of modules over commutative rings is also obtained.
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.