ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Structure
Algebraic structure
Identity element
Definition D536
Right inverse element
Formulation 0
Let $S = (X, +)$ be an D21: Algebraic structure such that
(i) \begin{equation} X \neq \emptyset \end{equation}
(ii) $0_S$ is an D39: Identity element in $S$
A D2218: Set element $y \in X$ is a right inverse element of $x \in X$ in $S$ if and only if \begin{equation} x + y = 0_S \end{equation}
Formulation 1
Let $S = (X, \times)$ be an D21: Algebraic structure such that
(i) \begin{equation} X \neq \emptyset \end{equation}
(ii) $1_S$ is an D39: Identity element in $S$
A D2218: Set element $y \in X$ is a right inverse element of $x \in X$ in $S$ if and only if \begin{equation} x y = 1_S \end{equation}
Formulation 2
Let $S = (X, f)$ be an D21: Algebraic structure such that
(i) \begin{equation} X \neq \emptyset \end{equation}
(ii) $I_S$ is an D39: Identity element in $S$
A D2218: Set element $y \in X$ is a right inverse element of $x \in X$ in $S$ if and only if \begin{equation} f(x, y) = I_S \end{equation}
Children
Right inverse map