The Nilpotent Regular Element Problem

Canadian mathematical bulletin

Pere Ara¹  Kevin C. O'Meara² 

[1] Department of Mathematics, Universitat Autònoma de Barcelona, 08193 Bellaterra (Bar?elona), Spain;2901 Gough Street, Apartment 302, San Francisco, CA 94123, USA

关键词: nilpotent element;    von Neumann regular element;    unit-regular;    Bergman's normal form;   

DOI  :  10.4153/CMB-2016-005-8

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

We use George Bergman's recent normal form for universally adjoining an inner inverse to show that, for general rings, a nilpotentregular 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 $x$ areregular.

【 授权许可】

Unknown