Opolka, Hans Norms in finite Galois extensions of the rationals. (English) Zbl 0686.12006 Int. J. Math. Math. Sci. 13, No. 4, 811-812 (1990). It is shown that, except for a certain special case, a rational number is a norm in a given finite Galois extension of the rationals if and only if this number is a local norm at a certain finite number of places in a certain finite abelian extension of the rationals. Reviewer: H.Opolka MSC: 11R37 Class field theory 11R04 Algebraic numbers; rings of algebraic integers Keywords:rational number; norm; finite Galois extension PDFBibTeX XMLCite \textit{H. Opolka}, Int. J. Math. Math. Sci. 13, No. 4, 811--812 (1990; Zbl 0686.12006) Full Text: DOI EuDML