5 papers · 1 filter
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…
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…
Gorenstein rings and irreducible parameter ideals
Thomas Marley, Mark W. Rogers, Hideto Sakurai
Given a Noetherian local ring (R,m) it is shown that there exists an integer l such that R is Gorenstein if and only if some system of parameters contained in m^l generates an irre…
The Index of Reducibility of Parameter Ideals and Mostly Zero Finite Local Cohomology
J. C. Liu, M. W. Rogers
We prove that if M is a finitely-generated module of dimension d with finite local cohomologies over a Noetherian local ring, and if the ith local cohomology module of M is zero un…
The index of reducibility of parameter ideals in low dimension
Mark W. Rogers
Results are presented concerning the following question: If M is a finitely-generated module with finite local cohomologies over a Noetherian local ring (A, m), does there exist an…