$n$-Torsion regular rings

Peter V. Danchev

Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2019), pp. 20-29.

Résumé

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–Šter (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.

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