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The Nilpotent Regular Element Problem

Published online by Cambridge University Press:  20 November 2018

Pere Ara  and
Kevin C. O'Meara
Pere Ara
Affiliation:
Department of Mathematics, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain e-mail: para@mat.uab.cat
Kevin C. O'Meara
Affiliation:
2901 Gough Street, Apartment 302, San Francisco, CA 94123, USA e-mail: staf198@ext.canterbury.ac.nz
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Abstract

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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.

Keywords

16E5016U9916S1016S15nilpotent elementvon Neumann regular elementunit-regularBergman's normal form
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 59 , Issue 3 , 01 September 2016 , pp. 461 - 471
Copyright
Copyright © Canadian Mathematical Society 2016

References

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