Completely simple endomorphism rings of modules

Victor Bovdi; Mohamed Salim; Mihail Ursul

doi:10.4995/agt.2018.7955

Completely simple endomorphism rings of modules

Victor Bovdi, Mohamed Salim, Mihail Ursul

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

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 modules over commutative rings is obtained.

Original language	English
Pages (from-to)	223-237
Number of pages	15
Journal	Applied General Topology
Volume	19
Issue number	2
DOIs	https://doi.org/10.4995/agt.2018.7955
Publication status	Published - 2018

Keywords

Bohr topology
Endomorphism ring
Finite topology
Locally compact ring
Topological ring

ASJC Scopus subject areas

Geometry and Topology

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10.4995/agt.2018.7955

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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 modules over commutative rings is obtained.",

keywords = "Bohr topology, Endomorphism ring, Finite topology, Locally compact ring, Topological ring",

author = "Victor Bovdi and Mohamed Salim and Mihail Ursul",

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AU - Ursul, Mihail

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N2 - 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.

AB - 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.

KW - Bohr topology

KW - Endomorphism ring

KW - Finite topology

KW - Locally compact ring

KW - Topological ring

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Completely simple endomorphism rings of modules

Abstract

Keywords

ASJC Scopus subject areas

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