\begin{definition}[Definition:Power-Associative Algebra]
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.
\end{definition}