# Definitions for **identity element**

### This page provides all possible meanings and translations of the word **identity element**

### Princeton's WordNet

identity, identity element, identity operator(noun)

an operator that leaves unchanged the element on which it operates

"the identity under numerical multiplication is 1"

### Wiktionary

identity element(Noun)

A member of a structure which, when applied to any other element via a binary operation induces an identity mapping; more specifically, given an operation *, an element I is

### Freebase

Identity element

In mathematics, an identity element is a special type of element of a set with respect to a binary operation on that set. It leaves other elements unchanged when combined with them. This is used for groups and related concepts. The term identity element is often shortened to identity when there is no possibility of confusion. Let be a set S with a binary operation ∗ on it. Then an element e of S is called a left identity if e ∗ a = a for all a in S, and a right identity if a ∗ e = a for all a in S. If e is both a left identity and a right identity, then it is called a two-sided identity, or simply an identity. An identity with respect to addition is called an additive identity and an identity with respect to multiplication is called a multiplicative identity. The distinction is used most often for sets that support both binary operations, such as rings. The multiplicative identity is often called the unit in the latter context, where, though, a unit is often used in a broader sense, to mean an element with a multiplicative inverse.

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"identity element." *Definitions.net.* STANDS4 LLC, 2014. Web. 30 Oct. 2014. <http://www.definitions.net/definition/identity element>.