Article

Algebras and Representation Theory

, Volume 15, Issue 1, pp 195-200

Open Access This content is freely available online to anyone, anywhere at any time.

Rings of Idempotent Stable Range One

  • Zhou WangAffiliated withDepartment of Mathematics, Southeast University Email author 
  • , Jianlong ChenAffiliated withDepartment of Mathematics, Southeast University
  • , Dinesh KhuranaAffiliated withFaculty of Mathematics, Indian Inst. of Sci. Edu. & Res.
  • , Tsit-Yuen LamAffiliated withDepartment of Mathematics, University of California

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