# Definition:Inverse (Abstract Algebra)/Left Inverse

This page is about Left Inverse Element in the context of Abstract Algebra. For other uses, see Left Inverse.

## Definition

Let $\struct {S, \circ}$ be a monoid whose identity is $e_S$.

An element $x_L \in S$ is called a left inverse of $x$ if and only if:

$x_L \circ x = e_S$

## Also see

• Results about inverse elements can be found here.