A Weak Hasse Principle for Central Simple Algebras with an Involution

The notions of totally indefinite and weakly isotropic algebras with involution are introduced and a proof is given of the fact that a field satisfies the Effective Diagonalization Property (ED) if and only if it satisfies the following weak Hasse principle: every totally indefinite central simple algebra with involution of the first kind over the given field is weakly isotropic. This generalizes a known result from quadratic form theory.

2000 Mathematics Subject Classification: 16K20, 11E39, 12J15

Keywords and Phrases: Real fields, central simple algebras, involutions, weak Hasse principles, hermitian squares

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