Artinʹs L-functions and one-dimensional characters Original Research Article

Let image be a finite Galois extension with the Galois group G, let χ1,…,χr be the irreducible non-trivial characters of G, and let image be the image-algebra generated by the Artin L-functions L(s,χ1),…,L(s,χr). Let image be the subalgebra of image generated by the L-functions corresponding to induced characters of non-trivial one-dimensional characters of subgroups of G. We prove: (1) image is of Krull dimension r and has the same quotient field as image; (2) image iff G is M-group; (3) the integral closure of image in image equals image iff G is quasi-M-group.