Submission: 2007, Apr 11, revised: 2007, Jul 31
It is shown that any split product of quaternion algebras with orthogonal involution is adjoint to a Pfister form. This settles the Pfister Factor Conjecture formulated by D. B. Shapiro. A more general problem on decomposability for algebras with involution is posed and solved in the case where the algebra is equivalent to a quaternion algebra.
2000 Mathematics Subject Classification:
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