Definition:Alternative Algebra

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Definition

Let $\left({A_R, \oplus}\right)$ be an algebra over a ring $R$.


Then $\left({A_R, \oplus}\right)$ is an alternative algebra if and only if $\oplus$ is alternative.


That is:

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


Sources