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Definition D535
Left inverse element

Let $S = (X, +)$ be an D21: Algebraic structure such that
 (i) $$X \neq \emptyset$$ (ii) $0_S$ is an D39: Identity element in $S$
A D2218: Set element $y \in X$ is a left inverse element of $x \in X$ in $S$ if and only if $$y + x = 0_S$$

Let $S = (X, \times)$ be an D21: Algebraic structure such that
 (i) $$X \neq \emptyset$$ (ii) $1_S$ is an D39: Identity element in $S$
A D2218: Set element $y \in X$ is a left inverse element of $x \in X$ in $S$ if and only if $$y x = 1_S$$

Let $S = (X, f)$ be an D21: Algebraic structure such that
 (i) $$X \neq \emptyset$$ (ii) $I_S$ is an D39: Identity element in $S$
A D2218: Set element $y \in X$ is a left inverse element of $x \in X$ in $S$ if and only if $$f(y, x) = I_S$$
Children
 ▶ Left inverse map