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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Quadratic spaces over Laurent extensions of Dedekind domains


Author: Raman Parimala
Journal: Trans. Amer. Math. Soc. 277 (1983), 569-578
MSC: Primary 11E12; Secondary 13C13, 18F25
MathSciNet review: 694376
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Abstract: Let $ R$ be a Dedekind domain in which $ 2$ is invertible. We show in this paper that any isotropic quadratic space over $ R[T,{T^{ - 1}}]$ is isometric to $ {q_1} \perp T{q_2}$ where $ {q_1},{q_2}$ are quadratic spaces over $ R$. We give an example to show that this result does not hold for anisotropic spaces.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1983-0694376-2
PII: S 0002-9947(1983)0694376-2
Keywords: Quadratic spaces, isotropy, Laurent-extensions, Dedekind domains
Article copyright: © Copyright 1983 American Mathematical Society