Definition:Inverse (Abstract Algebra)/Left Inverse

Definition
Let $\left({S, \circ}\right)$ be a monoid whose identity is $e_S$. An element $x_L \in S$ is called a left inverse of $x$ iff $x_L \circ x = e_S$.

Also see

 * Right Inverse
 * Inverse Element


 * Left Inverse for All is Right Inverse