The nilpotent regular element problem

Pere Ara; Kevin C. O'Meara

doi:10.4153/CMB-2016-005-8

The nilpotent regular element problem

Pere Ara, Kevin C. O'Meara

Research output: Contribution to journal › Article › Research › peer-review

2 Citations (Scopus)

Abstract

© Canadian Mathematical Society 2016. 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.

Original language	English
Pages (from-to)	461-471
Journal	Canadian Mathematical Bulletin
Volume	59
Issue number	3
DOIs	https://doi.org/10.4153/CMB-2016-005-8
Publication status	Published - 1 Sept 2016

Keywords

Bergman's normal form
Nilpotent element
Unit-regular
Von Neumann regular element

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10.4153/CMB-2016-005-8

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AB - © Canadian Mathematical Society 2016. 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.

KW - Bergman's normal form

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KW - Unit-regular

KW - Von Neumann regular element

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JO - Canadian Mathematical Bulletin

JF - Canadian Mathematical Bulletin

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The nilpotent regular element problem

Abstract

Keywords

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