More on rings of functions which are discontinuous on a set of measure zero

Abstract

Consider the ring Cc(X)F of real valued functions which are discontinuous on a finite set with countable range. We discuss (Zc)Ffilters on X and (Zc)F -ideals of Cc(X)F . We establish an analogous version of Gelfand-Kolmogoroff theorem in our setting. We prove some equivalent conditions when Cc(X)F is a Baer-ring and a regular ring. Lastly, we talk about the zero divisor graph on Cc(X)F .