| 1. | The algebra of bioctonions is an example of an octonion algebra.
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| 2. | But like the octonion product it is not uniquely defined.
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| 3. | In particular, this gives the classification of octonion algebras.
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| 4. | Moreover, the Moufang identities hold in any octonion algebra.
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| 5. | The Cayley plane uses octonion coordinates which do not satisfy the associative law.
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| 6. | There are corresponding split octonion algebras over any field " F ".
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| 7. | Instead there are many different cross products, each one dependent on the choice of octonion product.
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| 8. | This property is shared by most binary operations, but not subtraction or division or octonion multiplication.
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| 9. | This one is derived from its parent octonion ( one of 480 possible ), which is defined by:
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| 10. | The algebra of bioctonions is the octonion algebra over the complex numbers "'C " '.
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