Archimedean Clean f-rings
by
Warren Wm. McGovern
Bowling Green State University

An element of a ring is called clean if it may be written as a sum of a unit and an idempotent. If every element is clean then the ring is similarly called clean. It is known that a ring is a von-Neumann regular ring if and only if every element may be written as a product of a unit and an idempotent. It is straightforward to show that these rings are clean. Clean rings are in fact pm-rings; that is, rings in which every prime ideal is contained in a unique maximal ideal.

We shall discuss recent work in which archimedean clean f-rings are characterized using the maximal ideal space. We shall end the discussion by considering C(X) the ring of continuous real-valued functions on a Tychonoff space X. Other generalizations of the definition clean shall also play a part in the talk.

Date received: January 28, 2002

Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cain-04.