Abstract
For a Noetherian local ring (R, m) having a finite residue field of cardinality q, we study the connections between the ideal N (R) of R[x], which is the set of polynomials that vanish on R, and the ideal N(m), the polynomials that vanish on m, using polynomials of the form (formula presented) where c1,…, cq is a set of representatives of the residue classes of m. In particular, when R is Henselian we show that a generating set for N (R) may be obtained from a generating set for N (m) by composing with π(x).
Department(s)
Mathematics
Document Type
Article
DOI
https://doi.org/10.24330/ieja.325942
Rights Information
© 2017 the authors. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Keywords
Artinian ring, Finite ring, Null ideal, Polynomial function, Vanishing polynomial
Publication Date
1-1-2017
Recommended Citation
Rogers, Mark W., and Cameron Wickham. "Polynomials inducing the zero function on local rings." arXiv preprint arXiv:1607.02482 (2016).
Journal Title
International Electronic Journal of Algebra
