Polynomials inducing the zero function on chain rings

Abstract

We provide a minimal set of generators for the ideal of polynomials in [Formula: see text] that map the maximal ideal [Formula: see text] into one of its powers [Formula: see text], where [Formula: see text] is a discrete valuation ring with a finite residue field. We use this to provide a minimal set of generators for the ideal of polynomials in [Formula: see text] that send [Formula: see text] to zero, where [Formula: see text] is a finite commutative local principal ideal ring.