Title of article
zR-Ideals and z^0_R-Ideals in Subrings of R^X
Author/Authors
Rezaei Aliabad, Ali Department of Mathematics - Shahid Chamran University of Ahvaz, Ahvaz, Iran , Parsinia, Mehdi Department of Mathematics - Shahid Chamran University of Ahvaz, Ahvaz, Iran
Pages
13
From page
55
To page
67
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.
Keywords
in- vertible subring , Z(R)-topology , Coz(R)-topology , Growing ideal , z_R- ideal , z^0_R-ideal
Serial Year
2019
Record number
2494757
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