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Definition D39
Identity element

Let $S = (X, f)$ be an D21: Algebraic structure such that
 (i) $$X \neq \emptyset$$
A D2218: Set element $y \in X$ is an identity element in $S$ if and only if
 (1) $$\forall \, x \in X : f(y, x) = x$$ D537: Left identity element (2) $$\forall \, x \in X : f(x, y) = x$$ D538: Right identity element

Let $S = (X, \times)$ be an D21: Algebraic structure such that
 (i) $$X \neq \emptyset$$
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) $$X \neq \emptyset$$
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)
Children
 ▶ Inverse element ▶ Left inverse element ▶ Right inverse element