Fermat's Little Theorem and Euler's Theorem in a class of rings

Considering ${\mathbb{Z}}_n$ the ring of integers modulo $n$, the classical Fermat-Euler theorem establishes the existence of a specific natural number $\phi (n)$ satisfying the following property: $x^{\phi (n)}=1$ 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.