On a question of Hartwig and Luh

S. J. Dittmer; D. Khurana; P. P. Nielsen

On a question of Hartwig and Luh

Authors

S. J. Dittmer Brigham Young University
D. Khurana Panjab University
P. P. Nielsen Brigham Young University

Keywords:

Dedekind-finite rings, Dischinger's theorem, exchange rings, strongly $\pi$-regular rings

Abstract

In 1977 Hartwig and Luh asked whether an element

$a$ in a Dedekind-finite ring

$R$ satisfying

$aR = a^2R$ also satisfies

$Ra = Ra^2$ . In this paper, we answer this question in the negative. We also prove that if

$a$ is an element of a Dedekind-finite, exchange ring

$R$ and

$aR = a^2R$ then

$Ra = Ra^2$ . This gives an easier proof of Dischinger's theorem that left strongly

$\pi$ -regular rings are right strongly

$\pi$ -regular, when

$R$ is an exchange ring. 10.1017/S0004972713000373/a>

Published

2014-01-27

Issue

Vol. 89 No. 2 (2014)

Section

Articles

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