Let X be a topological space and R be a subring of RX. By determining some special topologies on X associated with
the subring R, characterizations of maximal fixxed and maximal
growing ideals in R of the form Mx(R) are given. Moreover, the
classes of zR-ideals and z0R-ideals are introduced in R which are
topological generalizations of z-ideals and z0-ideals of C(X), respectively. Various c...