Definition:Self-Inverse Element/Definition 2
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Definition
Let $\struct {S, \circ}$ be a monoid whose identity element is $e$.
Let $x \in S$ be an element of $S$.
$x$ is a self-inverse element of $\struct {S, \circ}$ if and only if:
- $x$ is invertible
and:
- $x = x^{-1}$, where $x^{-1}$ is the inverse of $x$.
Also known as
The definition of a self-inverse element is usually made in the context of a group.
Some sources refer to such an element as an involution.