Submission: 2017, Oct 10
Let E be a field which is the center of a quaternion division algebra and which is not real euclidean. Then there exists a biquaternion division alge- bra over the rational function field E(t) which does not contain any quaternion algebra defined over E. The proof is based on the study of Bezoutian forms developped in Becher-Raczek, `Ramification sequences and Bezoutian forms' (LAG-preprint 568).
2010 Mathematics Subject Classification: 12E30, 12G05, 12Y05, 19D45
Keywords and Phrases: field, Milnor K-theory, quadratic form, valuation, ramification, Bezoutian form
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