# Category:Definitions/Identity Elements

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This category contains definitions related to Identity Elements.

Related results can be found in **Category:Identity Elements**.

An element $e \in S$ is called an **identity (element)** if and only if it is both a left identity and a right identity:

- $\forall x \in S: x \circ e = x = e \circ x$

In Identity is Unique it is established that an **identity element**, if it exists, is unique within $\struct {S, \circ}$.

Thus it is justified to refer to it as ** the identity** (of a given algebraic structure).

This **identity** is often denoted $e_S$, or $e$ if it is clearly understood what structure is being discussed.

## Pages in category "Definitions/Identity Elements"

The following 19 pages are in this category, out of 19 total.