Karim Johannes Becher: Splitting fields of central simple algebras of exponent two


Submission: 2016, Mar 17

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.

2010 Mathematics Subject Classification: 11E04, 11E81, 16H05, 16K20, 16K50

Keywords and Phrases: Brauer group, field, central simple algebra, quaternion algebra, splitting field, index, exponent, 2-extension, involution

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