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.
@article{bwmeta1.element.ojs-doi-10_17951_a_2018_72_1_45-53,
author = {Peter V. Danchev},
title = {Invo-regular unital rings},
journal = {Annales Universitatis Mariae Curie-Sk\l odowska, sectio A -- Mathematica},
volume = {72},
year = {2018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2018_72_1_45-53}
}
Peter V. Danchev. Invo-regular unital rings. Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica, Tome 72 (2018) . http://gdmltest.u-ga.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2018_72_1_45-53/
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