English

Power sums over commutative and unitary rings

Rings and Algebras 2016-03-21 v1

Abstract

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

Keywords

Cite

@article{arxiv.1603.05787,
  title  = {Power sums over commutative and unitary rings},
  author = {Jose Maria Grau and Antonio. M. Oller-Marcen},
  journal= {arXiv preprint arXiv:1603.05787},
  year   = {2016}
}