\begin{definition}[Definition:Commutative Algebra]
Let $R$ be a commutative ring.
Let $\struct {A_R, \oplus}$ be an algebra over $R$.
Then $\struct {A_R, \oplus}$ is a commutative algebra {{iff}} $\oplus$ is a commutative operation.
That is:
:$\forall a, b \in A_R: a \oplus b = b \oplus a$
\end{definition}