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.

Location: http://mech.math.msu.su/~fpm/eng/k08/k082/k08210h.htm

Last modified: December 18, 2008