Completely simple endomorphism rings of modules-Reference-Cited by-同舟云学术

Completely simple endomorphism rings of modules

Published:2018-10-04 Issue:2 Volume:19 Page:223
ISSN:1989-4147
Container-title:Applied General Topology
language:
Short-container-title:Appl. Gen. Topol.

Author:

Bovdi Victor^ORCID,Salim Mohamed,Ursul Mihail^ORCID

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.

Publisher

Universitat Politecnica de Valencia

Subject

Geometry and Topology

Reference31 articles.

1. A. V. Arkhangelskii and V. I. Ponomarev, Osnovy obshchei topologii v zadachakh i uprazhneniyakh, Izdat. Nauka, Moscow, 1974.

2. V. I. Arnautov, S. T. Glavatsky and A. V. Mikhalev, Introduction to the theory of topological rings and modules, vol. 197 of Monographs and Textbooks in Pure and Applied Mathematics. Marcel Dekker, Inc., New York, 1996.

3. V. I. Arnautov and M. I. Ursul, Uniqueness of a linearly compact topology in rings, Mat. Issled. 53 (1979), 6-14, 221.

4. N. Bourbaki, Kommutativnaya algebra, Izdat. Mir, Moscow, 1971. Èlementy Matematiki, Vyp. XXVII, XXVIII, XXX, XXXI. [Foundations of Mathematics, No. XXVII, XXVIII, XXX, XXXI], Translated from the French by A. A. Belskii, Edited by E. S. Golod.

5. N. Bourbaki, General topology. Chapters 1-4. Elements of Mathematics (Berlin), Springer-Verlag, Berlin, 1998.

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