A characterization of c-type subrings of C(X) of some kind

A commutative ring with unity is of a c-type if it is (ring) isomorphic with C(X) for some space X. In this paper, we have described a structural representation of c-type subrings of C(X) that separates points and contains the constant function 1, but not necessarily containing C*(X). It would be complete if all c-type subring of C(X) separate points and contains 1. But, we have produced an example of c-type ring which does not separate points. We have also produced an example of a subring of C(R) not containing C*(R) which is of c-type, R real line.