Invo-regular unital rings

Peter V. Danchev

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

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References


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DOI: http://dx.doi.org/10.17951/a.2018.72.1.45-53
Date of publication: 2018-06-25 09:04:05
Date of submission: 2018-06-24 22:15:17


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