STRONGLY -CLEAN PROPERTIES AND RINGS OF FUNCTIONS

Authors : Huanyin CHEN, Abdullah HARMANCI

Pages : 102-115

Doi:10.1501/Commua1_0000000834

View : 17 | Download : 10

Publication Date : 2018-02-01

Article Type : Research Paper

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 Cinsert ignore into journalissuearticles values(X); C insert ignore into journalissuearticles values(X); is-clean, if and only if R isan abelian exchange ring and the classical ring of quotients qinsert ignore into journalissuearticles values(Cinsert ignore into journalissuearticles values(X);); of Cinsert ignore into journalissuearticles values(X);is -clean, where X is a spectrum space of R
Keywords : Strongly clean ring, ring of continuous functions, topological space