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 a left identity element in $S$ if and only if \begin{equation} \forall \, x \in X : y + x = x \end{equation}

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 a left identity element in $S$ if and only if \begin{equation} \forall \, x \in X : y x = x \end{equation}

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 a left identity element in $S$ if and only if \begin{equation} \forall \, x \in X : f(y, x) = x \end{equation}