Definition:Power of Element/Monoid/Invertible Element

Definition
Let $\left({S, \circ}\right)$ be a monoid whose identity element is $e$. Let $b \in S$ be invertible for $\circ$.

Let $n \in \Z$.

The definition $b^n = \circ ^n \left({b}\right)$ as the $n$th power of $b$ in $\left({S, \circ}\right)$ can be extended to include the inverse of $b$:


 * $b^{-n} = \left({b^{-1}}\right)^n$