Property: unit regular

Definition: For every $x$, there exists a unit $u$ such that $x=xux$

Resources for learning about this property:

  • A. A. Tuganbaev. Semidistributive modules and rings. (2012) @ Chapter 3
  • K. R. Goodearl. Von Neumann regular rings. (1991) @ Chapter 4

Metaproperties:

This property has the following metaproperties
  • passes to quotient rings
  • stable under products
  • stable under finite products
  • Morita invariant