Author/Authors :
Rogers, Mark W Department of Mathematics - Missouri State University, USA , Wickham, Cameron Department of Mathematics - Missouri State University, USA
Abstract :
For a Noetherian local ring pR, mq having a finite residue field of
cardinality q, we study the connections between the ideal N pRq of Rrxs, which
is the set of polynomials that vanish on R, and the ideal N pmq, the polynomials
that vanish on m, using polynomials of the form πpxq ±q
i1
px ciq, 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 pRq may be obtained
from a generating set for N pmq by composing with πpxq.
