کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5778047 | 1633061 | 2017 | 13 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Gelfand-Kolmogoroff theorem for rings of analytic functions
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
هندسه و توپولوژی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
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.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 218, 1 March 2017, Pages 53-65
Journal: Topology and its Applications - Volume 218, 1 March 2017, Pages 53-65
نویسندگان
Bedanta Bose, Mayukh Mukherjee,