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Witts Theorem for Quadratic Forms Over Non-Dyadic Discrete Valuation Rings

Published online by Cambridge University Press:  20 November 2018

David Mordecai Cohen
David Mordecai Cohen*
Affiliation:
University of California, Irvine, California
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Let R be a discrete valuation ring, with maximal ideal pR, such that ½ ϵ R. Let L be a finitely generated R-module and B : L × L → R a non-degenerate symmetric bilinear form. The module L is called a quadratic module. For notational convenience we shall write xy = B(x, y). Let O(L) be the group of isometries, i.e. all R-linear isomorphisms φ : L → L such that B((φ(x), (φ(y)) = B(x, y).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 5 , 01 October 1977 , pp. 928 - 936
Copyright
Copyright © Canadian Mathematical Society 1977

References

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