STRONGLY *-CLEAN PROPERTIES AND RINGS OF FUNCTIONS

Abstract

A *-ring R is called a strongly *-clean ring if every element ofR is the sum of a unit and a projection that commute with each other. Inthis paper, we explore strong *-cleanness of rings of continuous functions overspectrum spaces. We prove that a *-ring R is strongly *-clean if and only if Ris an abelian exchange ring and $C(X) 􀀀C(X)$is *-clean, if and only if R isan abelian exchange ring and the classical ring of quotients $q(C(X)) of C(X)$is *-clean, where X is a spectrum space of R.