Property: division ring

Definition: all nonzero elements are units

Resources for learning about this property:

  • T.-Y. Lam. A first course in noncommutative rings. (2013) @ Chapter 5

Metaproperties:

This property has the following metaproperties
  • passes to $eRe$ for any full idempotent $e$
  • passes to the center
  • passes to quotient rings
This property does not have the following metaproperties