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Volume 10
Issue 19
10.3390/math10193479
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Article

Prime Spectrum of the Ring of Adeles of a Number Field

by
Álvaro Serrano Holgado
Department of Mathematics, University of Salamanca, Plaza de la Merced 1, 37008 Salamanca, Spain
Mathematics 2022, 10(19), 3479; https://doi.org/10.3390/math10193479
Submission received: 24 August 2022 / Revised: 14 September 2022 / Accepted: 20 September 2022 / Published: 23 September 2022
(This article belongs to the Section A: Algebra and Logic)
Versions Notes

Abstract

Much is known about the adele ring of an algebraic number field from the perspective of harmonic analysis and class field theory. However, its ring-theoretical aspects are often ignored. Here, we present a description of the prime spectrum of this ring and study some of the algebraic and topological properties of these prime ideals. We also study how they behave under separable extensions of the base field and give an indication of how this study can be applied in adele rings not of number fields.
Keywords: adele ring; prime spectrum; ultrafilters; topological rings adele ring; prime spectrum; ultrafilters; topological rings

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MDPI and ACS Style

Serrano Holgado, Á. Prime Spectrum of the Ring of Adeles of a Number Field. Mathematics 2022, 10, 3479. https://doi.org/10.3390/math10193479

AMA Style

Serrano Holgado Á. Prime Spectrum of the Ring of Adeles of a Number Field. Mathematics. 2022; 10(19):3479. https://doi.org/10.3390/math10193479

Chicago/Turabian Style

Serrano Holgado, Álvaro. 2022. "Prime Spectrum of the Ring of Adeles of a Number Field" Mathematics 10, no. 19: 3479. https://doi.org/10.3390/math10193479

APA Style

Serrano Holgado, Á. (2022). Prime Spectrum of the Ring of Adeles of a Number Field. Mathematics, 10(19), 3479. https://doi.org/10.3390/math10193479

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