FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

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

Rings over which all modules are I0-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(AA). It is proved that all A-modules are I0-modules if and only if either A is a right semi-Artinian right V-ring or A/SI(AA) is an Artinian serial ring and the square of the Jacobson radical of A/SI(AA) is equal to zero.

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