Algebras and Representation Theory

, Volume 15, Issue 1, pp 195–200

Rings of Idempotent Stable Range One

  • Zhou Wang
  • Jianlong Chen
  • Dinesh Khurana
  • Tsit-Yuen Lam
Open AccessArticle

DOI: 10.1007/s10468-011-9276-4

Cite this article as:
Wang, Z., Chen, J., Khurana, D. et al. Algebr Represent Theor (2012) 15: 195. 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 oneStable range oneRegular elementsUnit regular ringsClean rings

Mathematics Subject Classifications (2010)

16D7016E50
Download to read the full article text

Copyright information

© The Author(s) 2011

Authors and Affiliations

  • Zhou Wang
    • 1
  • Jianlong Chen
    • 1
  • Dinesh Khurana
    • 2
  • Tsit-Yuen Lam
    • 3
  1. 1.Department of MathematicsSoutheast UniversityNanjingPeople’s Republic of China
  2. 2.Faculty of MathematicsIndian Inst. of Sci. Edu. & Res.ChandigarhIndia
  3. 3.Department of MathematicsUniversity of CaliforniaBerkeleyUSA