You are here

Rings of integer-valued polynomials and derivatives

Download pdf | Full Screen View

Date Issued:
2012
Summary:
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.
Title: Rings of integer-valued polynomials and derivatives.
156 views
27 downloads
Name(s): Villanueva, Yuri.
Charles E. Schmidt College of Science
Department of Mathematical Sciences
Type of Resource: text
Genre: Electronic Thesis Or Dissertation
Date Issued: 2012
Publisher: Florida Atlantic University
Physical Form: electronic
Extent: v, 43 p.
Language(s): English
Summary: 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.
Identifier: 820554826 (oclc), 3356899 (digitool), FADT3356899 (IID), fau:3995 (fedora)
Note(s): by Yuri Villanueva.
Thesis (Ph.D.)--Florida Atlantic University, 2012.
Includes bibliography.
Mode of access: World Wide Web.
System requirements: Adobe Reader.
Subject(s): Rings of integers
Ideals (Algebra)
Polynomials
Arithmetic algebraic geometry
Categories (Mathematics)
Commutative algebra
Persistent Link to This Record: http://purl.flvc.org/FAU/3356899
Use and Reproduction: http://rightsstatements.org/vocab/InC/1.0/
Host Institution: FAU