\begin{definition}[Definition:Operation/Binary Operation/Product]
Let $\struct {S, \circ}$ be an algebraic structure.
Let $\circ$ be the operation on $\struct {S, \circ}$.
Let $z = x \circ y$.
Then $z$ is called the '''product''' of $x$ and $y$.
This is an extension of the normal definition of product that is encountered in conventional arithmetic.
\end{definition}