Splitting fields of central simple algebras of exponent two

By Merkurjev's Theorem every central simple algebra of exponent two is Brauer equivalent to a tensor product of quaternion algebras. In particular, if every quaternion algebra over a given field is split, then there exists no central simple algebra of exponent two over this field. This note provides an independent elementary proof for the latter fact. (C) 2016 Elsevier B.V. All rights reserved.