z_R-Ideals and z^0_R-Ideals in Subrings of R^X

Abstract

pspan style=font-family:tahoma;span style=font-size:14px;Let X be a topological space and R be a subring of RsupstrongX/strong/sup. By determining some special topologies on X associated withbr the subring R, characterizations of maximal fixxed and maximal growing ideals in R of the form Msubx/sub(R) are given. Moreover, thebr classes of zsubR/sub-ideals and zsup0/supsubR/sub-ideals are introduced in R which arenbsp;topological generalizations of z-ideals and zsup0/sup-ideals of C(X), respectively. Various characterizations of these ideals are established,nbsp;also, coincidence of zsubR/sub-ideals with z-ideals and zsubR/sub-ideals with z-ideals in R are investigated. It turns out that some fundamentalnbsp;statements in the context of C(X) are extended to the subrings of RsupX/sup/span/span/p