Polynomials inducing the zero function on chain rings
Abstract
We provide a minimal set of generators for the ideal of polynomials in R[x] that map the maximal ideal into one of its powers n, where (R,) 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 to zero, where (R,) is a finite commutative local principal ideal ring.
Department(s)
Mathematics
Document Type
Article
DOI
https://doi.org/10.1142/S0219498818501608
Keywords
Artinian rings, chain ring, discrete valuation ring, Finite ring, polynomial functions, vanishing polynomials
Publication Date
8-1-2018
Recommended Citation
Rogers, Mark W., and Cameron Wickham. "Polynomials inducing the zero function on chain rings." Journal of Algebra and Its Applications 17, no. 08 (2018): 1850160.
Journal Title
Journal of Algebra and its Applications
COinS
