Invo-regular unital rings
Journal Title: Annales Universitatis Mariae Curie-Skłodowska. Sectio A, Mathematica - Year 2018, Vol 72, Issue 1
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 ˇSter 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.
Authors and Affiliations
Peter Danchev
Keywords
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- EP ID EP530443
- DOI 10.17951/a.2018.72.1.45
- Views 91
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