Open Access
Article

Algebras and Representation Theory

, Volume 15, Issue 1, pp 195-200

Rings of Idempotent Stable Range One

Authors

  • Zhou Wang
    • Department of MathematicsSoutheast University
  • Jianlong Chen
    • Department of MathematicsSoutheast University
  • Dinesh Khurana
    • Faculty of MathematicsIndian Inst. of Sci. Edu. & Res.
  • Tsit-Yuen Lam
    • Department of MathematicsUniversity of California

DOI: 10.1007/s10468-011-9276-4

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.

Keywords

Idempotent stable range one Stable range one Regular elements Unit regular rings Clean rings

Mathematics Subject Classifications (2010)

16D70 16E50

Copyright information

© The Author(s) 2011