Definition:Alternative Algebra

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Definition

Let $\struct {A_R, \oplus}$ be an algebra over a ring $R$.


Then $\struct {A_R, \oplus}$ is an alternative algebra if and only if $\oplus$ is an alternative operation.


That is:

For all $a, b \in A_R$, the subalgebra generated by $\set {a, b}$ is an associative algebra.


Sources