When Gelfand Rings are Clean

In this paper, we consider a special class of ideals of a commu- tative ring called lifting ideals and comaximal factorizations of ideals of a ring into this class of ideals. Then by using Pierce stalks we characterize the Gelfand rings whose ideals can be written as a product of comaximal lifting ideals. Finaly, we characterize completely regular topological spaces X such that C(X) is a clean ring.