Property: semisimple

Definition: semiprimitive and Artinian

Resources for learning about this property:

  • F. W. Anderson and K. R. Fuller. Rings and categories of modules. (2012) @ Chapter 4
  • K. R. Goodearl and R. B. W. Jr. An introduction to noncommutative Noetherian rings. (2004) @ Chapter 4
  • T.-Y. Lam. A first course in noncommutative rings. (2013) @ Chapter 1


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