Witt equivalence of central simple algebras with involution

The notion of Witt equivalence of central simple algebras with involution is introduced. It is shown that the standard invariants, i.e. the discriminant, the signature and the Clifford algebra, depend only on the Witt class of the algebra with involution. For a given filedF the tensor product is used to construct a semigroup\(\tilde S\left( F \right)\) and this semigroup is shown to have properties analogous to the multiplicative properties of the Witt ring of quadratic forms overF.