Alternative Algebra

In abstract algebra, an alternative algebra is an algebra in which multiplication need not be associative, only alternative. That is, one must have

for all x and y in the algebra. Every associative algebra is obviously alternative, but so too are some strictly nonassociative algebras such as the octonions. The sedenions, on the other hand, are not alternative.

Read more about Alternative Algebra:  The Associator, Properties, Applications

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