 The most familiar example of a ring is the set of all integers, formula_1, consisting of the numbers

The familiar properties for addition and multiplication of integers serve as a model for the axioms for rings.A ring is a set "R" equipped with two binary operations + and · satisfying the following three sets of axioms, called the ring axioms


As explained in below, many authors follow an alternative convention in which a ring is not defined to have a multiplicative identity.This article adopts the convention that, unless otherwise stated, a ring is assumed to have such an identity.