Matematičeskie zametki, Tome 75 (2004) no. 6, pp. 895-908
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A. A. Tuganbaev. Modules over Endomorphism Rings. Matematičeskie zametki, Tome 75 (2004) no. 6, pp. 895-908. http://geodesic.mathdoc.fr/item/MZM_2004_75_6_a7/
@article{MZM_2004_75_6_a7,
author = {A. A. Tuganbaev},
title = {Modules over {Endomorphism} {Rings}},
journal = {Matemati\v{c}eskie zametki},
pages = {895--908},
year = {2004},
volume = {75},
number = {6},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_2004_75_6_a7/}
}
TY - JOUR
AU - A. A. Tuganbaev
TI - Modules over Endomorphism Rings
JO - Matematičeskie zametki
PY - 2004
SP - 895
EP - 908
VL - 75
IS - 6
UR - http://geodesic.mathdoc.fr/item/MZM_2004_75_6_a7/
LA - ru
ID - MZM_2004_75_6_a7
ER -
%0 Journal Article
%A A. A. Tuganbaev
%T Modules over Endomorphism Rings
%J Matematičeskie zametki
%D 2004
%P 895-908
%V 75
%N 6
%U http://geodesic.mathdoc.fr/item/MZM_2004_75_6_a7/
%G ru
%F MZM_2004_75_6_a7
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.
