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Communications in Algebra Volume 43, 2015 - Issue 5
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Original Articles

Uniquely Clean Elements in Rings

Dinesh Khurana Department of Mathematics, Panjab University, Chandigarh, India
,
T. Y. Lam Department of Mathematics, University of California, Berkeley, California, USA
,
Pace P. Nielsen Department of Mathematics, Brigham Young University, Provo, Utah, USACorrespondence[email protected]
&
Yiqiang Zhou Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, Newfoundland, Canada
Pages 1742-1751 | Received 15 Aug 2013, Published online: 27 Feb 2015
 
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Abstract

It is well known that every uniquely clean ring is strongly clean. In this article, we investigate the question of when this result holds element-wise. We first construct an example showing that uniquely clean elements need not be strongly clean. However, in case every corner ring is clean the uniquely clean elements are strongly clean. Further, we classify the set of uniquely clean elements for various classes of rings, including semiperfect rings, unit-regular rings, and endomorphism rings of continuous modules.

2010 Mathematics Subject Classification:

Notes

Communicated by J. L. Gomez Pardo.

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