Algebras and Representation Theory

, Volume 15, Issue 1, pp 195–200

Rings of Idempotent Stable Range One

Authors

    • 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
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
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Copyright information

© The Author(s) 2011