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Page 205 of the book Classical Groups and Algebraic K-Theory defines a symplectic module to be an arbitrary quadratic module $(M,h,q)$ over a form ring $(R,\Lambda)$ with $(J,\varepsilon)$ where $J=\operatorname{id}_R$, $\varepsilon=-1$ and $\Lambda=R$. In particular, this implies that $R$ is com...
