# Definition:Inverse (Abstract Algebra)/Right Inverse

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

## Definition

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

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

$x \circ x_R = e_S$