Inverse Element

algebra

Definition

Inverse Element

The inverse element $x^{\prime }\in S$ of an element $x\in S$ of a relation $\circ$ over a set $S$ is called inverse element iff:

$$\forall x\in S:\exists x^{\prime }\in S:x\circ x^{\prime }=x^{\prime }\circ x=e$$

Note that $e$ denotes the neutral element.