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\(n\)-torsion regular rings. (English) Zbl 1428.16012

Summary: 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 P. P. Nielsen and J. Šter [Trans. Am. Math. Soc. 370, No. 3, 1759–1782 (2018; Zbl 1445.16008)] 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.

MSC:

16E50 von Neumann regular rings and generalizations (associative algebraic aspects)
16U60 Units, groups of units (associative rings and algebras)

Citations:

Zbl 1445.16008
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References:

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