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:

$x \circ x_R = e_S$

Also see

• Definition:Left Inverse Element
• Definition:Inverse Element

• Right Inverse for All is Left Inverse

Sources

• 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text I$: Algebraic Structures: $\S 4$: Neutral Elements and Inverses: Exercise $4.9$
• 1966: Richard A. Dean: Elements of Abstract Algebra ... (previous) ... (next): $\S 1.2$
• 1968: Ian D. Macdonald: The Theory of Groups ... (previous) ... (next): $\S 1$: Some examples of groups