A note on semicentral idempotents

ABSTRACT

In this note we answer the question raised by Han et al. in [3] 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.

KEYWORDS:

• Dedekind-finite rings
• idempotents
• semicentral idempotents

2000 MATHEMATICS SUBJECT CLASSIFICATION:

• 17C27
• 16U99
• 16S50

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.