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Mat. Zametki, 2004, Volume 75, Issue 6, Pages 895–908 (Mi mz79)  

Modules over Endomorphism Rings

A. A. Tuganbaev

Moscow Power Engineering Institute (Technical University)

Abstract: It is proved that $A$ is a right distributive ring if and only if all quasiinjective right $A$-modules are Bezout left modules over their endomorphism rings if and only if for any quasiinjective right $A$-module $M$ which is a Bezout left $\operatorname{End}(M)$-module, every direct summand $N$ of $M$ is a Bezout $\operatorname{End}(M)$-module. If $A$ is a right or left perfect ring, then all right $A$-modules are Bezout left modules over their endomorphism rings if and only if all right $A$-modules are distributive left modules over their endomorphism rings if and only if $A$ is a distributive ring.

DOI: https://doi.org/10.4213/mzm79

Full text: PDF file (218 kB)
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English version:
Mathematical Notes, 2004, 75:6, 836–847

Bibliographic databases:

UDC: 512.55
Received: 20.12.2001

Citation: A. A. Tuganbaev, “Modules over Endomorphism Rings”, Mat. Zametki, 75:6 (2004), 895–908; Math. Notes, 75:6 (2004), 836–847

Citation in format AMSBIB
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\issue 6
\pages 836--847
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