SEMICLEAN RINGS AND RINGS OF CONTINUOUS FUNCTIONS

摘要

As defined by Ye [12], a ring is semiclean if every element is the sum of a unit and a periodic element. Ahn and Anderson [1] called a ring weakly clean if every element can be written as u + e or u ? e, where u is a unit and e an idempotent. A weakly clean ring is semiclean. We show the existence of semiclean rings that are not weakly clean. Every semiclean ring is 2-clean. New classes of semiclean subrings of R and C are introduced and conditions are given when these rings are clean. Cleanliness and related properties of C(X,A) are studied when A is a dense semiclean subring of R or C.