Submission: 2003, Jan 10
A formula is given for the discriminant of the tensor product of the canonical involution on a quaternion algebra and an orthogonal involution on a central simple algebra of degree divisible by 4. As an application, an alternative proof of Shapiro's ``Pfister Factor Conjecture'' is given for tensor products of at most five quaternion algebras.
2000 Mathematics Subject Classification: 11E72, 11E81
Keywords and Phrases: central simple algebra with involution, Pfister form
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