On Quasi-Baer Rings
by
Jae Keol Park
Department of Mathematics, Busan National University, Busan 609-735, Korea

Recall that a ring R is quasi-Baer if the right annihilator of every right ideal is generated by an idempotent as a right ideal. Quasi-Baer rings are initially considered by W. E. Clark to characterize a finite dimensional algebra over an algebraically closed field to be isomorphic to a twisted semigroup algebra of a matrix unit semigroup. We discuss several results for quasi-Baer rings and apply our results to functional analysis which can be compared with some results in Baer rings. Also we show that every piecewise domain is a quasi-Baer ring. One our interesting result is that quasi-Baerness is a Morita invariant property. Furthermore we consider a sheaf representation of quasi-Baer rings, thereby we completely characterize piecewise domains which can have a certain sheaf representation.

Date received: December 30, 1998