ABSTRACT
In this note we answer the question raised by Han et al. in [Citation3] whether an idempotent isomorphic to a semicentral idempotent is itself semicentral. We show that rings with this property are precisely the Dedekind-finite rings. An application to module theory is given.
Acknowledgment
This work was done during a visit of the first author to the University of Warsaw. He would like to thank the second author and all members of the Mathematics Department for their warm hospitality.