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math.AC2016
Polynomials Inducing the Zero Function on Local Rings
Mark W. Rogers, Cameron Wickham
For a Noetherian local ring (R, m) having a finite residue field of cardinality q, we study the connections between the ideal Z(R) of R[x], which is the set of polynomials that van…
math.AC2016
Sets of Lengths of Powers of a Variable
Richard Belshoff, Daniel Kline, Mark W. Rogers
A positive integer k is a length of a polynomial if that polynomial factors into a product of k irreducible polynomials. We find the set of lengths of polynomials of the form x^n i…