کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8897480 | 1630741 | 2018 | 10 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On the spectrum of rings of functions
ترجمه فارسی عنوان
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
چکیده انگلیسی
For D a domain and EâD, we investigate the prime spectrum of rings of functions from E to D, that is, of rings contained in âeâED and containing D. Among other things, we characterize, when M is a maximal ideal of finite index in D, those prime ideals lying above M which contain the kernel of the canonical map to âeâE(D/M) as being precisely the prime ideals corresponding to ultrafilters on E. We give a sufficient condition for when all primes above M are of this form and thus establish a correspondence to the prime spectra of ultraproducts of residue class rings of D. As a corollary, we obtain a description using ultrafilters, differing from Chabert's original one which uses elements of the M-adic completion, of the prime ideals in the ring of integer-valued polynomials Int(D) lying above a maximal ideal of finite index.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Pure and Applied Algebra - Volume 222, Issue 8, August 2018, Pages 2089-2098
Journal: Journal of Pure and Applied Algebra - Volume 222, Issue 8, August 2018, Pages 2089-2098
نویسندگان
Sophie Frisch,