%0 Journal Article
%T Filters of Coz(X)
%J Categories and General Algebraic Structures with Applications
%I Shahid Beheshti University
%Z 2345-5853
%A Bhattacharjee, Papiya
%A M. Drees, Kevin
%D 2017
%\ 07/01/2017
%V 7
%N Special Issue on the Occasion of Banaschewski's 90th Birthday (II)
%P 107-123
%! Filters of Coz(X)
%K Cozero sets
%K ultrafilters
%K minimal prime ideals
%K $P$-space
%K $F$-space
%K inverse topology
%K $ell$-groups
%R
%X In this article we investigate filters of cozero sets for real-valued continuous functions, called $coz$-filters. Much is known for $z$-ultrafilters and their correspondence with maximal ideals of $C(X)$. Similarly, a correspondence will be established between $coz$-ultrafilters and minimal prime ideals of $C(X)$. We will further notice various properties of $coz$-ultrafilters in relation to $P$-spaces and $F$-spaces. In the last two sections, the collection of $coz$-ultrafilters will be topologized, and then compared to the hull-kernel and the inverse topologies placed on the collection of minimal prime ideals of $C(X)$ and general lattice-ordered groups.
%U https://cgasa.sbu.ac.ir/article_44925_013d795e3961eac0b6b094ece513d81e.pdf