Definition:Invertible Element

Definition
Let $$\left({S, \circ}\right)$$ be an algebraic structure which has an identity $$e_S$$.

If $$x \in S$$ has an inverse, then $$x$$ is said to be invertible for $$\circ$$.

That is, $$x$$ is invertible iff:


 * $$\exists y \in S: x \circ y = e_S = y \circ x$$

Also see
In the context of a ring $$\left({R, +, \circ}\right)$$, an element that is invertible in the semigroup $$\left({R, \circ}\right)$$ is called a unit of $$\left({R, +, \circ}\right)$$.