Geodesic
$n$-Torsion regular rings
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2019), pp. 20-29

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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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     author = {Peter V. Danchev},
     title = {$n${-Torsion} regular rings},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {20--29},
     publisher = {mathdoc},
     number = {1},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2019_1_a1/}
}
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Peter V. Danchev. $n$-Torsion regular rings. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2019), pp. 20-29. http://geodesic.mathdoc.fr/item/BASM_2019_1_a1/