en تخصصي Special پژوهشي Research paper <br> <p></p> <p><span style="font-family:tahoma;"><span style="font-size:14px;">Let X be a topological space and R be a subring of R^{<strong>X</strong>}. By determining some special topologies on X associated with<br> the subring R, characterizations of maximal fixxed and maximal growing ideals in R of the form M_x(R) are given. Moreover, the<br> classes of z_R-ideals and z⁰_R-ideals are introduced in R which are&nbsp;topological generalizations of z-ideals and z⁰-ideals of C(X), respectively. Various characterizations of these ideals are established,&nbsp;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&nbsp;statements in the context of C(X) are extended to the subrings of R^X</span></span></p> Z(R)-topology, Coz(R)-topology, Growing ideal, z_R- ideal, z^0_R-ideal, Invertible subring. 55 67 http://ijmsi.ir/browse.php?a_code=A-10-2011-1&slc_lang=en&sid=1 A. Rezaei Aliabad 10031947532846007035 10031947532846007035 No Shahid Chamran University of Ahvaz M. parsinia parsiniaemhdi@gmail.com 10031947532846007036 10031947532846007036 Yes Shahid Chamran University of Ahvaz