\begin{definition}[Definition:Associative Algebra]
Let $R$ be a commutative ring.
Let $\left({A_R, *}\right)$ be an algebra over $R$.
Then $\left({A_R, *}\right)$ is an '''associative algebra''' {{iff}} $*$ is an associative operation.
That is:
:$\forall a, b, c \in A_R: \left({a * b}\right) * c = a * \left({b * c}\right)$
\end{definition}