We prove that von Neumann regularity is not a Morita invariant property for non-unital rings. This contrasts heavily with the unital case. Moreover, we give an internal characterization of the idempotent rings which are Morita equivalent to a von Neumann regular ring. We also show that an s-unital ring Morita equivalent to a von Neumann regular ring is von Neumann regular too. © AMSS CAS 2004.
|Publication status||Published - 1 Dec 2004|
- Morita equivalence
- Non-unital rings
- Von Neumann regular rings