Azumaya algebras with involution

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One of the highpoints of the theory of central simple algebras as developed in the 1920s and 1930s was the results of Albert concerning simple rings with involution. A part of his results was the characterization of those finite dimensional central simple algebras which admit an involution. This characterization was extended and clarified by Scharlau [8] and Tamagawa (unpublished). It is our intention here to generalize this result in the context of Azumaya algebras over commutative rings. We obtain conditions parallel to the classical ones as to when the equivalence class of an Azumaya algebra contains an algebra with involution. In the last section, we improve and clarify our result in three special cases; Azumaya algebras of rank 4, trivial Azumaya algebras, and Azumaya algebras over connected semilocal rings. Contained in the arguments of this paper is a new proof of the classical result.