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Abstract

The main object in this chapter (from Section 7.2 onwards) is a quadratic space (M,q) that is decomposed into a direct sum of a totally isotropic submodule U such that U = U, and any supplementary submodule V. Thus (M,q) is hyperbolic (see (2.5.5)) even if V is not totally isotropic, and d q induces canonical isomorphisms U → (M/U)* → V* and VM/UU* (see (2.3.7)). As a quadratic module, V will also interest us, and the short notation (V, q) (instead of (V, q|v)) will be preferred; it is clear that the quadratic form q on M is determined by its restriction to V and by the above isomorphism UV*.

Keywords

Bilinear Form Local Ring Direct Summand Hyperbolic Space Left Ideal 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag AG 2008

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