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

Section

Articles