STRONGLY -CLEAN PROPERTIES AND RINGS OF FUNCTIONS

Abstract

ARis 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