Byott, Nigel P.; Elder, G. Griffith Biquadratic extensions with one break. (English) Zbl 1033.11054 Can. Math. Bull. 45, No. 2, 168-179 (2002). Let \(K\) be a finite extension of the field of \(2\)-adic numbers, and consider totally ramified biquadratic extensions \(N/K\) with Galois group \(G\). The ramification filtration of \(G\) (with lower numbering) contains one or two breaks; the Galois module structure of ideals in extensions with two breaks were studied by the second author [Can. J. Math. 50, 1007–1047 (1998; Zbl 1015.11056)]. In this article, the authors treat the more complicated case of fields with one break and show explicitly how the ideals \({\mathfrak P}^i\) in \(N\) decompose into indecomposable \({\mathbb Z}_2[G]\)-modules. Reviewer: Franz Lemmermeyer (Bilkent) Cited in 1 ReviewCited in 3 Documents MSC: 11S15 Ramification and extension theory 11R33 Integral representations related to algebraic numbers; Galois module structure of rings of integers 20C11 \(p\)-adic representations of finite groups Keywords:Galois module structure; local fields; ramification groups Citations:Zbl 1015.11056 PDFBibTeX XMLCite \textit{N. P. Byott} and \textit{G. G. Elder}, Can. Math. Bull. 45, No. 2, 168--179 (2002; Zbl 1033.11054) Full Text: DOI