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Galois Module Structure of the Integers in Wildly Ramified Cp × Cp Extensions

Published online by Cambridge University Press:  20 November 2018

G. Griffith Elder  and
Manohar L. Madan
G. Griffith Elder
Affiliation:
The Department of Mathematics, The Ohio State University, 231 W. 18th Avenue, Columbus, Ohio 43210, U.S.A.
Manohar L. Madan
Affiliation:
The Department of Mathematics, The University of Nebraska at Omaha, Omaha, Nebraska 68182, U.S.A.
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Abstract

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Let L/K be a finite Galois extension of local fields which are finite extensions of ℚp, the field of p-adic numbers. Let Gal(L/K) = G, and 𝔒L and ℤp be the rings of integers in L and ℚp, respectively. And let 𝔓L denote the maximal ideal of 𝔒L. We determine, explicitly in terms of specific indecomposable ℤp[G]-modules, the ℤp[G]-module structure of 𝔒L and 𝔓L, for L, a composite of two arithmetically disjoint, ramified cyclic extensions of K, one of which is only weakly ramified in the sense of Erez [6].

Keywords

11S1520C32Galois module structure–integral representation
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 49 , Issue 4 , 01 August 1997 , pp. 722 - 735
Copyright
Copyright © Canadian Mathematical Society 1997

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