Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5778047 | Topology and its Applications | 2017 | 13 Pages |
Abstract
Consider rings of single variable real analytic or complex entire functions, denoted by Kãzã. We study “discrete z-filters” on K and their connections with the space of maximal ideals of Kãzã. 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 βKâQ(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 Kãzã and show that the Krull dimension of Kãzã 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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Bedanta Bose, Mayukh Mukherjee,