Definition:Power-Associative Algebra

Definition

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

Then $\struct {A_R, \oplus}$ is a power-associative algebra if and only if $\oplus$ is power-associative.

That is:

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

Also see

• Results about power-associative algebras can be found here.

Sources

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