Power sums over finite commutative unital rings

In this paper we compute the sum of the k-th powers of all the elements of a finite commutative unital ring, 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 (Z/nZ)[x]/(f(x)) for a polynomial f∈Z[x].