En matemáticas, y particularmente en álgebra abstracta, el elemento neutro o elemento identidad de un conjunto A, dotado de una operación binaria interna : es un elemento e del conjunto, tal que para cualquier otro elemento a del conjunto se cumple: Es decir, un elemento neutro tiene un efecto neutro al ser utilizado en la operación . Al operar cualquier elemento del conjunto con el elemento neutro el resultado es el elemento original. Un elemento e que cumpla solamente e a = a se llama elemento neutro por la izquierda. Análogamente un elemento f que cumple solamente a f = a se llama o se denomina elemento neutro por la derecha. No tienen que ser iguales dichos elementos, salvo el caso de un grupo. Pueden existir los dos, uno de ellos o ninguno en el caso de un conjunto provisto de una operación.

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In mathematics, an identity element or neutral element is a special type of element of a set with respect to a binary operation on that set, which leaves other elements unchanged when combined with them. This concept is used in algebraic structures such as groups. The term identity element is often shortened to identity (as will be done in this article) when there is no possibility of confusion. Let (S, ∗) 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 (often denoted as 0) and an identity with respect to multiplication is called a multiplicative identity (often denoted as 1). 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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