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Invo-regular unital rings

Author(s) -

Peter Danchev

Publication year - 2018

Publication title -

annales universitatis mariae curie-sklodowska sectio a – mathematica

Language(s) - English

Resource type - Journals

eISSN - 2083-7402

pISSN - 0365-1029

DOI - 10.17951/a.2018.72.1.45-53

Subject(s) - unit (ring theory) , unital , mathematics , class (philosophy) , von neumann regular ring , ring (chemistry) , commutative ring , a priori and a posteriori , subclass , commutative property , commutative algebra , pure mathematics , algebra over a field , computer science , chemistry , mathematics education , artificial intelligence , philosophy , antibody , organic chemistry , epistemology , immunology , biology

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.

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