Definition:Alternative Algebra
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.
