Definition:Power-Associative Algebra

Definition
Let $\left({A_R, \oplus}\right)$ be an algebra over a ring $R$.

Then $\left({A_R, \oplus}\right)$ is a power-associative algebra iff $\oplus$ is power-associative.

That is:


 * For all $a \in A_R$, the subalgebra generated by $\left\{{a}\right\}$ is an associative algebra.