Article ID Journal Published Year Pages File Type
5778047 Topology and its Applications 2017 13 Pages PDF
Abstract
Consider rings of single variable real analytic or complex entire functions, denoted by K〈z〉. We study “discrete z-filters” on K and their connections with the space of maximal ideals of K〈z〉. We characterize the latter as a compact T1 space θK of discrete z-ultrafilters on K. We show that θK is a bijective continuous image of βK∖Q(K), where Q(K) is the set of far points of βK. θK turns out to be the Wallman compactification of the canonically embedded image of K inside θK. Using our characterization of θK, we derive a Gelfand-Kolmogoroff characterization of maximal ideals of K〈z〉 and show that the Krull dimension of K〈z〉 is at least c. We also establish the existence of a chain of prime z-filters on K consisting of at least 2c many elements.
Related Topics
Physical Sciences and Engineering Mathematics Geometry and Topology
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