FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2007, VOLUME 13, NUMBER 5, PAGES 193-200

Rings over which all modules are $I$₀-modules

A. A. Tuganbaev

Abstract

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Let $A$ be a ring that does not contain an infinite set of idempotents that are orthogonal modulo the ideal $SI(A$_A). It is proved that all $A$-modules are $I$₀-modules if and only if either $A$ is a right semi-Artinian right V-ring or $A/SI(A$_A) is an Artinian serial ring and the square of the Jacobson radical of $A/SI(A$_A) is equal to zero.

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Last modified: February 18, 2008