Power sums over commutative and unitary rings

In this paper we compute the sum of the $k$-th powers over any finite commutative unital rings, thus generalizing known results for finite fields, the rings of integers modulo $n$ or the ring of Gaussian integers modulo $n$. As an application we focus on quotient rings of the form $\mathbb{Z}\mathrm{/}n\mathbb{Z}[x]\mathrm{/}(f(x))$ for any polynomial $f\in \mathbb{Z}[x]$