Definition:Operation/Binary Operation/Product

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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.


Left-Hand Product

Let $x$ and $y$ be elements which are operated on by a given operation $\circ$.

The left-hand product of $x$ by $y$ is the product $y \circ x$.


Right-Hand Product

Let $x$ and $y$ be elements which are operated on by a given operation $\circ$.

The right-hand product of $x$ by $y$ is the product $x \circ y$.


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.


Sources