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Rings of integervalued polynomials and derivatives
 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 integervalued 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, onedimensional, analytically irreducible, with finite residue field.
Title:  Rings of integervalued polynomials and derivatives. 
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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 integervalued 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, onedimensional, 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 