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IMI/Publicaţii/BASM/Ediţii/BASM n.1(89), 2019/

n-Torsion Regular Rings

Authors: P. V. Danchev

Abstract

As proper subclasses of the classes of unit-regular and strongly regular rings, respectively, the two new classes of $n$-torsion regular rings and strongly $n$-torsion regular rings are introduced and investigated for any natural number $n$. Their complete isomorphism classification is given as well. More concretely, although it has been recently shown by Nielsen-\v{S}ter (TAMS, 2018) that unit-regular rings need not be strongly clean, the rather curious fact that, for each positive odd integer $n$, the $n$-torsion regular rings are always strongly clean is proved.

Institute of Mathematics and Informatics,
Bulgarian Academy of Sciences,
1113 Sofia, Bulgaria
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