Author Type

Graduate Student

Date of Award

2012

Document Type

Thesis

Publication Status

Version of Record

Submission Date

October 2026

Abstract

For D an integral domain with field of fractions K and E a subset of K, the ring Int (E,D) = {f e K[X]lf (E) C D} of integer-valued polynomials on E has been well studies. In particulare, when E is a finite subset of D, Chapman, Loper, and Smith, as well as Boynton and Klingler, obtained a bound on the number of elements needed to generate a finitely generated ideal of Ing (E, D) in terms of the corresponding bound for D. We obtain analogous results for Int (r) (E, D) - {f e K [X]lf(k) (E) c D for all 0 < k < r} , for finite E and fixed integer r > 1. These results rely on the work of Skolem [23] and Brizolis [7], who found ways to characterize ideals of Int (E, D) from the values of their polynomials at points in D. We obtain similar results for E = D in case D is local, Noetherian, one-dimensional, analytically irreducible, with finite residue field.

Extent

v, 43 p.

Comments

by Yuri Villanueva.|Thesis (Ph.D.)--Florida Atlantic University, 2012.|Includes bibliography.|Mode of access: World Wide Web.|System requirements: Adobe Reader.|by Yuri Villanueva.

Identifier

FADT3356899

Format

pdf

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