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Algebras and Representation Theory

, Volume 15, Issue 1, pp 195–200 | Cite as

Rings of Idempotent Stable Range One

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

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