On Topological Spaces X Determined by the Torsion Elements of C(X)

Let C(X) be the ring of real continuous functions on a Tychonoff space X and T(X) be the set of all torsion elements of C(X). We prove that if X and Y are two zero dimensional compact spaces, then X ʹ Y if and only if the rings generated by T(X) and T(Y ) are isomorphic.