A note on the Artin map
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.
scientific article; zbMATH DE number 4164999
scientific article