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 $\oplus$ is power-associative.

That is:


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