Property: semiprime

Definition: No nonzero nilpotent right ideals

Resources for learning about this property:

  • T.-Y. Lam. A first course in noncommutative rings. (2013) @ Chapter 4
  • T.-Y. Lam. Lectures on modules and rings. (2012) @ Sections 11B, 14A


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