FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2008, VOLUME 14, NUMBER 2, PAGES 207-221

Rings without infinite sets of noncentral orthogonal idempotents

A. A. Tuganbaev

Abstract

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Let $A$ be a ring without infinite sets of noncentral orthogonal idempotents. $A$ is an exchange ring if and only if all Pierce stalks of $A$ are semiperfect rings. All $A$-modules are $I$₀-modules if and only if either $A$ is a right semi-Artinian ring in which every proper right ideal is the intersection of maximal right ideals or $A/SI(A$_A) is an Artinian serial ring such that the square of the Jacobson radical of $A/SI(A$_A) is equal to zero.

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Last modified: December 18, 2008