Definition:Operation/Binary Operation/Product

Definition
For a given operation $\circ$, 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.

Also known as
The product of $a$ and $b$ is sometimes seen referred to as their sum.

This can be confusing and is therefore endorsed on this site only when referring to ring addition.