High Quality Content by WIKIPEDIA articles! Fix a field k. All vector spaces will be assumed to be finite-dimensional. We say that two symmetric bilinear forms are equivalent if one can be obtained from the other by adding zero or more copies of a hyperbolic plane. The Witt group of k is the abelian group of equivalence classes of non-degenerate symmetric bilinear forms, with the group operation corresponding to the orthogonal direct sum of forms. The Witt group of k can be given a commutative ring structure, by using the tensor product of two bilinear forms to define the ring product. This is sometimes called the Witt ring of k, though the term "Witt ring" is often also used for a completely different ring of Witt vectors.

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