Completely simple endomorphism rings of modules

2017/12/26 by Victor Bovdi, Bovdi, V. A., Mohamed Salim +3
Mathematics · #16N20 #16N40 #16S50 #16W80 #FOS: Mathematics #General Topology (math.GN) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1712.09186

openalex publication_date 2017/12/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• On the endomorphism rings of abelian groups and their Jacobson radical
• The endomorphism ring of the trivial module in a localized category
• On Endo-trivial Modules for p-Solvable Groups
• Endomorphism rings of simple modules and block decomposition
• On endomorphism rings of local cohomology