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

Voir la notice de l'article provenant de la source Cambridge University Press

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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