, Volume 15, Issue 1, pp 195-200,
Open Access This content is freely available online to anyone, anywhere at any time.
Date: 22 Feb 2011

Rings of Idempotent Stable Range One

Abstract

We show that in a ring of stable range 1, any (von Neumann) regular element is clean. Our main results also imply that any unit-regular ring has idempotent stable range 1 (and is therefore clean), and that a semilocal ring has idempotent stable range 1 if and only if it is semiperfect.

Presented by Kenneth Goodearl.