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.

Sources

• John C. Baez: The Octonions (2002): 1.1 Preliminaries