Product (mathematics)

From Ref

The term product is typically used for the result obtained on performing a multiplication. Here, the multiplication is a binary operation on a set or structure. The multiplication is usually taken to be associative (so that parenthesization does not matter for the product) and often taken to be commutative (so that the order of terms doesn't matter).

Typical uses in elementary mathematics

Product of numbers

Product of functions

In a semigroup, monoid or group

Product in a semigroup

Product in a ring

In a category

Direct product of groups

Direct product in a variety of algebras

Categorical product