Title

Polynomials inducing the zero function on local rings

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

Journal Title

International Electronic Journal of Algebra

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