2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68458Two Azumaya algebras with involutions are considered over a regular local ring. It is proved that if they are isomorphic over the quotient field, then they are isomorphic too. In particular, if two quadratic spaces over such a ring are similar over its quotient field, then these two spaces are similar already over the ring. The result is a consequence of a purity theorem for similarity factors proved in this text and the known fact that rationally isomorphic hermitian spases are locally isomorphic.22 pagesAlgebraic GeometryK-Theory and Homology11E72text