An Isomorphism Problem for Azumaya Algebras with Involution over Semilocal Bézout Domains
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Let R be a semilocal Bézout domain with fraction field F. Assume that 2 is invertible in R. The main result of this article states that R−algebras with involution that become isomorphic over F are already isomorphic over R. We also show that this implies that hermitian or skew-hermitian spaces over an R−algebra with involution without zero divisors that become similar over F, are already similar over R.
KeywordsAzumaya algebras with involution Central simple algebras with involution Algebraic groups Valuation rings Semilocal Bézout domains (skew-)hermitian spaces Bilinear spaces Multipliers
Mathematics Subject Classifications (2010)16H05 16K20 12J20 20G35
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