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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

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