Let X be a topological space and R be a subring of R^{X}. 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 M_{x}(R) are given. Moreover, the

classes of z_{R}-ideals and z^{0}_{R}-ideals are introduced in R which are

topological generalizations of z-ideals and z^{0}-ideals of C(X), respectively. Various characterizations of these ideals are established,

also, coincidence of z_{R}-ideals with z-ideals and z_{R}-ideals with z-ideals in R are investigated. It turns out that some fundamental

statements in the context of C(X) are extended to the subrings of R^{X}

Type of Study: Research paper |
Subject:
Special