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

Sources

• Seth Warner: Modern Algebra (1965)... (previous)... (next): Exercise $4.9$