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In the case of quadratic forms over a field, it is well-known that the primespectrum of the Witt ring and the space of orderings of the field determine oneanother, through associated signature maps. We show that a sililar relationholds for hermitian forms over algebras with involution of the first kind,replacing the usual Witt ring with the mixed Witt ring of such an algebra.

An Artin-Schreier-type theory for signatures of hermitian forms over involutions