Volume 14, Issue 1 (4-2019)                   IJMSI 2019, 14(1): 55-67 | Back to browse issues page

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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 characterizations of these ideals are established,
also, coincidence of zR-ideals with z-ideals and zR-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 RX

Type of Study: Research paper | Subject: Special