The nilpotent regular element problem

Pere Ara, Kevin C. O'Meara

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)


© 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 languageEnglish
Pages (from-to)461-471
JournalCanadian Mathematical Bulletin
Issue number3
Publication statusPublished - 1 Sept 2016


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


Dive into the research topics of 'The nilpotent regular element problem'. Together they form a unique fingerprint.

Cite this