Regular elements in P.I.-rings

Israel (Yitzchak) Nathan Herstein and Lance W. Small

Vol. 36 (1971), No. 2, 327–330

DOI: 10.2140/pjm.1971.36.327

Abstract

It follows from the proof of Posner’s theorem that half-regular elements are regular in prime rings satisfying a polynomial identity (prime P. I.-rings). In this paper we extend these results to semi-prime rings and present counterexamples to several avenues of further generalization.

Mathematical Subject Classification

Primary: 16.49

Milestones

Received: 8 September 1970

Published: 1 February 1971