Quadratic spaces over Laurent extensions of Dedekind domains

Parimala, Raman

doi:10.1090/S0002-9947-1983-0694376-2

Quadratic spaces over Laurent extensions of Dedekind domains
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Trans. Amer. Math. Soc. 277 (1983), 569-578 Request permission

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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