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ON A QUESTION OF HARTWIG AND LUH

  • SAMUEL J. DITTMER (a1), DINESH KHURANA (a2) and PACE P. NIELSEN (a3)
Abstract

In 1977 Hartwig and Luh asked whether an element $a$ in a Dedekind-finite ring $R$ satisfying $aR= {a}^{2} R$ also satisfies $Ra= R{a}^{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 $aR= {a}^{2} R$ , then $Ra= R{a}^{2} $ . This gives an easier proof of Dischinger’s theorem that left strongly $\pi $ -regular rings are right strongly $\pi $ -regular, when it is already known that $R$ is an exchange ring.

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Corresponding author
pace@math.byu.edu
References
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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