Ring

In modern algebra, a set of elements with two operations, referred to as “addition” and “multiplication,” that conform to certain conditions.

These specify that the set is closed under both operations, the associative law holds for both operations, the commutative law holds for addition, the distributive law holds, there is an additive identity (known as zero), and every element has an additive inverse (&see; inverse function). The set of integers is a ring. &Seealso; field theory.