Property: prime

Definition: The product of nonzero right ideals is nonzero

Resources for learning about this property:

  • T.-Y. Lam. A first course in noncommutative rings. (2013) @ Chapter 4


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