Polynomials Inducing the Zero Function on Local Rings

Mark W. Rogers, Missouri State University
Cameron Wickham

Abstract

We provide a minimal set of generators for the ideal of polynomials in R[x] that map the maximal ideal m into one of its powers mn, where (R,m) 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 R[x] that send m to zero, where (R,m) is a finite commutative local principal ideal ring.