Geodesic
The Nilpotent Regular Element Problem
Canadian mathematical bulletin, Tome 59 (2016) no. 3, pp. 461-471

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DOI

We use George Bergman's recent normal form for universally adjoining an inner inverse to show that, for general rings, a nilpotent regular element $x$ need not be unit-regular. This contrasts sharply with the situation for nilpotent regular elements in exchange rings (a large class of rings), and for general rings when all powers of the nilpotent element $x$ are regular.
DOI : 10.4153/CMB-2016-005-8
Mots-clés : 16E50, 16U99, 16S10, 16S15, nilpotent element, von Neumann regular element, unit-regular, Bergman's normal form 
Ara, Pere; O'Meara, Kevin C. The Nilpotent Regular Element Problem. Canadian mathematical bulletin, Tome 59 (2016) no. 3, pp. 461-471. doi: 10.4153/CMB-2016-005-8
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