Property: exchange

Definition: If $a+b=1$, there exists $r$ and $s$ such that $ar$ and $bs$ are idempotents and $ar+bs=1$

Resources for learning about this property:

  • A. A. Tuganbaev. Rings close to regular. (2013) @ Chapter 6
  • T.-Y. Lam. A crash course on stable range, cancellation, substitution and exchange. (2004) @ .


This property has the following metaproperties
  • passes to $eRe$ for any full idempotent $e$
  • passes to $eRe$ for any idempotent $e$