ArticleOriginal scientific text
Title
Invo-regular unital rings
Authors
Abstract
It was asked by Nicholson (Comm. Algebra, 1999) whether or not unit-regular rings are themselves strongly clean. Although they are clean as proved by Camillo-Khurana (Comm. Algebra, 2001), recently Nielsen and Ster showed in Trans. Amer. Math. Soc., 2018 that there exists a unit-regular ring which is not strongly clean. However, we define here a proper subclass of rings of the class of unit-regular rings, called invo-regular rings, and establish that they are strongly clean. Interestingly, without any concrete indications a priori, these rings are manifestly even commutative invo-clean as defined by the author in Commun. Korean Math. Soc., 2017.
Keywords
Unit-regular rings, clean rings, strongly clean rings, idempotents, involutions, nilpotents, units
Bibliography
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Main language of publication
English
Published
2018
Published online
2018-06-25
Exact and natural sciences