Brinkhuis, Jan Unramified abelian extensions of CM-fields and their Galois module structure. (English) Zbl 0768.11045 Bull. Lond. Math. Soc. 24, No. 3, 236-242 (1992). From the author’s introduction: “In the author’s previous paper [J. Reine Angew. Math. 375/376, 157-166 (1987; Zbl 0609.12009)], a non- existence result was given for normal integral bases of abelian extensions of CM-fields which are unramified at all finite primes. The aim of this paper is to give an account which gives, moreover, some information on the class \(({\mathfrak o}_ N)_ D\) of the \(D\)-module \({\mathfrak o}_ N\) (where \(D = {\mathfrak o}_ K[\text{Gal}(N/K)]\)) in the locally free class group \(C\ell(D)\) and on its order. The outcome generalizes the result in the former paper. In the present approach, one does not need the assumption that the top field \(N\) is CM”. Reviewer: T.Nguyen Quang Do (Besançon) Cited in 2 ReviewsCited in 7 Documents MSC: 11R33 Integral representations related to algebraic numbers; Galois module structure of rings of integers Keywords:normal integral bases; abelian extensions; locally free class group Citations:Zbl 0609.12009 PDFBibTeX XMLCite \textit{J. Brinkhuis}, Bull. Lond. Math. Soc. 24, No. 3, 236--242 (1992; Zbl 0768.11045) Full Text: DOI