A set equipped with operations addition , negation, multiplication, and often a 1 as an identity element of the multiplication, where the addition is associative and commutative and has the negation as its inverse, and the multiplication distributed over the addition. Sometimes people don’t always require that they include a unit for the multiplication.

An example of a ring is the set of integers, as is the set of integers mod 6, as is any field. A non-example is the set of non-negative integers.