  Considering $\mathbb{Z}_n$ the ring of integers modulo $n$, the classical
Fermat-Euler theorem establishes the existence of a specific natural number
$\varphi(n)$ satisfying the following property: $
x^{\varphi(n)}=1%\hspace{1.0cm}\text{for all}\hspace{0.2cm}x\in \mathbb{Z}_n^*,
$ for all $x$ belonging to the group of units of $\mathbb{Z}_n$. In this
manuscript, this result is extended to a class of rings that satisfies some
mild conditions.
