Let $S = (X, f)$ be an D21: Algebraic structure such that

(i)	\begin{equation} X \neq \emptyset \end{equation}

A D2218: Set element $y \in X$ is an identity element in $S$ if and only if

(1)	\begin{equation} \forall \, x \in X : f(y, x) = x \end{equation}	D537: Left identity element
(2)	\begin{equation} \forall \, x \in X : f(x, y) = x \end{equation}	D538: Right identity element

Let $S = (X, \times)$ be an D21: Algebraic structure such that

(i)	\begin{equation} X \neq \emptyset \end{equation}

A D2218: Set element $y \in X$ is an identity element in $S$ if and only if

(1)	$\forall \, x \in X : y x = x$	(D537: Left identity element)
(2)	$\forall \, x \in X : x y = x$	(D538: Right identity element)

Let $S = (X, +)$ be an D21: Algebraic structure such that

(i)	\begin{equation} X \neq \emptyset \end{equation}

A D2218: Set element $y \in X$ is an identity element in $S$ if and only if

(1)	\begin{equation} \forall \, x \in X : y + x = x \end{equation}	(D537: Left identity element)
(2)	\begin{equation} \forall \, x \in X : x + y = x \end{equation}	(D538: Right identity element)