Submission: 2010, Dec 26
Any two decompositions of a biquaternion algebra over a field $F$ into a sum of two quaternion algebras can be connected by a chain of decompositions such that any two neighboring decompositions are $(a,b)+(c,d)$ and $(ac,b)+(c,bd)$ for some $a,b,c,d\in F^*$. A similar result is established for decompositions of a biquaternion algebra into a sum of three quaternions if $F$ has no cubic extension.
2010 Mathematics Subject Classification:
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