Abstract: In 1988, J.R. Faulkner has given a procedure to construct an octonion algebra on a finite dimensional unitary alternative algebra of degree three over a field K. Here we use a similar procedure to get a quaternion algebra. Then we obtain some conditions for these octonion and quaternion algebras to be split or division algebras. Then we consider the implications of the found conditions to the underlying algebra, when K contains a cubic root of unity.
Keywords: Alternative algebra; Composition algebra; Division algebra; Flexible algebra; Hurwitz algebra; Power associative algebra.
Classification (MSC2000): 17D05; 17D99
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