A note on the Artin map
type: Item
instance of: scholarly article
title: A note on the Artin map
zbMATH Open document ID: 0709.11062
author: Takashi Ono
published in: Proceedings of the Japan Academy. Series A
publication date: 1989-01-01T00:00:00Z
review text: Let K/k be a finite Galois extension of number fields with Galois group G. The author defines a ``generalized Artin map'' \(\alpha_{K/k}: I(K/k)\to {\mathbb{C}}[G]_ 0\), where I(K/k) denotes the monoid of nonzero integral ideals of k whose prime factors are unramified in K and \({\mathbb{C}}[G]_ 0\) denotes the center of the group ring \({\mathbb{C}}[G]\). He obtains necessary and sufficient conditions for the finiteness of the image of \(\alpha_{K/k}\) in terms of the irreducible characters of G.
Mathematics Subject Classification ID: 11R37
Mathematics Subject Classification ID: 11R32
Mathematics Subject Classification ID: 12F10
Mathematics Subject Classification ID: 20C05
zbMATH DE Number: 4164999
zbMATH Keywords: class field theory
zbMATH Keywords: Galois extension of number fields
zbMATH Keywords: generalized Artin map
reviewed by: Hans Opolka
MaRDI profile type: Publication
full work available at URL: pjaa.65.304
OpenAlex ID: W1963593046
DOI: 10.3792/PJAA.65.304
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description: scientific article; zbMATH DE number 4164999