z_R-Ideals and z^0_R -Ideals in Subrings of R^X
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Abstract:
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
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Journal title
volume 14 issue 1
pages 55- 67
publication date 2019-04
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