Witt group

Summary

The Witt group of a field $F$ of characteristic not $2$ is an abelian group built from the nondegenerate quadratic forms over $F$. Two forms give the same element when they differ only by hyperbolic planes, and the group operation is the orthogonal sum. It collects the essential information about quadratic forms over $F$ into one algebraic object. With the tensor product of forms it becomes a ring, the Witt ring.