TY - JOUR
T1 - z_R-Ideals and z^0_R -Ideals in Subrings of R^X
TT -
JF - IJMSI
JO - IJMSI
VL - 14
IS - 1
UR - http://ijmsi.ir/article-1-896-en.html
Y1 - 2019
SP - 55
EP - 67
KW - Z(R)-topology
KW - Coz(R)-topology
KW - Growing ideal
KW - z_R- ideal
KW - z^0_R-ideal
KW - Invertible subring.
N2 - 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
M3
ER -