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Some self-dual local rings of integers not free over their associated orders

Published online by Cambridge University Press:  24 October 2008

N. P. Byott
N. P. Byott
Affiliation:
New College, Oxford
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Extract

Let p be a prime number, and let K be a finite extension of the rational p-adic field ℚp. Let L/K be a finite abelian extension with Galois group G, and let L, K denote the valuation rings of L, K respectively. Then L is a free module of rank 1 over the group algebra KG. Defining the associated order of the extension L/K by

L can be viewed as a module over the ring , and a fortiori over the group ring KG.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 110 , Issue 1 , July 1991 , pp. 5 - 10
Copyright
Copyright © Cambridge Philosophical Society 1991

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References

REFERENCES

[1]Bergé, A-M.. Arithmétique d'une extension galoisienne à groupe d'inertie cyclique. Ann. Inst. Fourier (Grenoble) 28 (1978), 17–44.CrossRefGoogle Scholar
[2]Burns, D.. Private communication with the author (1990).Google Scholar
[3]Cassou-Noguès, Ph. and Taylor, M. J.. Elliptic Functions and Rings of Integers. Progress in Mathematics vol. 66 (Birkhauser, 1987).Google Scholar
[4]Ferton, M. J.. Sur les idéaux d'une extension cyclique de degré premier d'un corps local. C. R. Acad. Sci. Paris 276 (1973), A1483–A1486.Google Scholar
[5]Martel, B.. Sur l'anneau des entiers d'une extension biquadratique d'un corps 2-adique. C. R. Acad. Sci. Paris 278 (1974), A117–A120.Google Scholar
[6]Serre, J-P.. Local Fields. Graduate Texts in Mathematics no. 67 (Springer-Verlag, 1979).CrossRefGoogle Scholar
[7]Washington, L. C.. Introduction to Cyclotomic Fields. Graduate Texts in Mathematics no. 83 (Springer-Verlag, 1982).CrossRefGoogle Scholar