In a set X equipped with a binary operation · called a product, the multiplicative identity is an element e such that e·x = x·e = x for all x element X. It can be, for example, the identity element of a multiplicative group or the unit of a unit ring. In both cases it is usually denoted 1. The number 1 is, in fact, the multiplicative identity of the ring of integers Z and of its extension rings such as the ring of Gaussian integers Z[i], the field of rational numbers Q, the field of real numbers R, and the field of complex numbers C. The residue class 1^_ of number 1 is the multiplicative identity of the quotient ring Z_n of Z for all integers n>1.

additive identity | multiplicative inverse