Geodesic
Invo-regular unital rings
Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 72 (2018) no. 1.

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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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Danchev, Peter V. Invo-regular unital rings. Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 72 (2018) no. 1. http://geodesic.mathdoc.fr/item/AUM_2018_72_1_a1/

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