How to Obtain Division Algebras from a Generalized Cayley-dickson Doubling Process
نویسنده
چکیده
We generalize the classical Cayley-Dickson doubling process starting with a quaternion algebra over a field F by allowing the scalar in the doubling to be an invertible element in the algebra. We investigate the resulting eight-dimensional algebras over F and show that they are division algebras for all scalars chosen in D outside of the base field F , if D is a division algebra.
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