Definition:Inverse (Abstract Algebra)/Right Inverse

Definition

Let $\left({S, \circ}\right)$ be a monoid whose identity is $e_S$.

An element $x_R \in S$ is called a right inverse of $x$ iff $x \circ x_R = e_S$.

Also see

• Left Inverse
• Inverse Element

• Left Inverse for All is Right Inverse

Sources

• Seth Warner: Modern Algebra (1965)... (previous)... (next): Exercise $4.9$
• Richard A. Dean: Elements of Abstract Algebra (1966): $\S 1.2$