Property: clean

Definition: Every element is the sum of a unit and an idempotent

Resources for learning about this property:

  • N. A. Immormino. Clean rings \& clean group rings. (2013) @ .
  • T.-Y. Lam. A crash course on stable range, cancellation, substitution and exchange. (2004) @ .
  • W. K. Nicholson and Y. Zhou. Clean rings: a survey. (2005) @ .


This property has the following metaproperties
  • stable under finite products
  • stable under products
  • passes to matrix rings
  • passes to quotient rings
This property does not have the following metaproperties