\begin{definition}[Definition:Alternative Algebra]
Let $\struct {A_R, \oplus}$ be an algebra over a ring $R$.
Then $\struct {A_R, \oplus}$ is an alternative algebra {{iff}} $\oplus$ is an alternative operation.
That is:
:For all $a, b \in A_R$, the subalgebra generated by $\set {a, b}$ is an associative algebra.
\end{definition}