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Biquadratic Extensions with One Break

Published online by Cambridge University Press:  20 November 2018

Nigel P. Byott  and
G. Griffith Elder
Nigel P. Byott
Affiliation:
School of Mathematical Sciences, University of Exeter, Exeter EX4 4QE, United Kingdom, e-mail: N.P.Byott@exeter.ac.uk
G. Griffith Elder
Affiliation:
Department of Mathematics, University of Nebraska at Omaha, Omaha, Nebraska 68182-0243, U.S.A., e-mail: elder@unomaha.edu
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Abstract

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We explicitly describe, in terms of indecomposable ${{\mathbb{Z}}_{2}}\left[ G \right]$ -modules, the Galois module structure of ideals in totally ramified biquadratic extensions of local number fields with only one break in their ramification filtration. This paper completeswork begun in [Elder: Canad. J.Math. (5) 50(1998), 1007–1047].

Keywords

11S1520C11

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 45 , Issue 2 , 01 June 2002 , pp. 168 - 179
Copyright
Copyright © Canadian Mathematical Society 2002

References

[Eld98] Elder, G. G., Galois module structure of ideals in wildly ramified biquadratic extensions. Canad. J. Math. (5) 50 (1998), 50–1998.Google Scholar
[Naz61] Nazarova, L. A., Integral representations of Klein's four-group. Soviet Math. Dokl. 2 (1961), 2–1961.Google Scholar
[Naz67] Nazarova, L. A., Representation of a Tetrad. Math. USSR-Izv. (6) 1 (1967), 1–1967.Google Scholar
[Ser79] Serre, J.-P., Local fields. Springer-Verlag, New York, 1979.Google Scholar