Prime Spectrum of the Ring of Adeles of a Number Field

Álvaro Serrano Holgado ()
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Álvaro Serrano Holgado: Department of Mathematics, University of Salamanca, Plaza de la Merced 1, 37008 Salamanca, Spain

Mathematics, 2022, vol. 10, issue 19, 1-11

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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