Submission: 2013, Jan 8. The final publication is available at
We show that rationally isomorphic Azumaya algebras with involution over a semilocal Bézout domain in which 2 is invertible are already isomorphic. As a corollary we obtain, that ``rational similarity implies similarity'' for epsilon-hermitian spaces over an Azumaya algebra with involution without zero divisors over a semilocal Bézout domain in which 2 is a unit. In the case of a semilocal principal ideal domain we give an easierproof of the ``rational isomorphism implies isomorphism'' property, using a Cassels--Pfister type result for certain algebras with involution.
2010 Mathematics Subject Classification: 16H05, 16W10, 16W60, 11E39
Keywords and Phrases: Azumaya algebras with involution over a semilocal Bézout domain, hermitian spaces, adjoint involutions, rationally isomorphic.
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