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Pruefer domains, the strong 2generator property, and integervalued polynomials
 Date Issued:
 2004
 Summary:
 We present several results involving three concepts: Prufer domains, the strong 2generator property, and integervalued polynomials. An integral domain D is called a Prufer domain if every nonzero finitely generated ideal of D is invertible. When each 2generated ideal of D has the property that one of its generators can be any arbitrary selected nonzero element of the ideal, we say D has the strong 2generator property . We note that, if D has the strong 2generator property, then D is a Prufer domain. If Q is the field of fractions of D, and E is a finite nonempty subset of D; we define Int(E, D ) = {f(X) ∈ Q[ X] ∣ f(a) ∈ D for every a ∈ E} to be the ring of integervalued polynomials on D with respect to the subset E. We show that D is a Prufer domain if and only if Int(E, D) is a Prufer domain. Our main theorem is that Int(E, D) has the strong 2generator property if and only if D is a Bezout domain (that is, every finitely generated ideal of D is principal).
Title:  Pruefer domains, the strong 2generator property, and integervalued polynomials. 
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Name(s): 
Roth, Heather. Florida Atlantic University, Degree grantor Klingler, Lee, Thesis advisor 

Type of Resource:  text  
Genre:  Electronic Thesis Or Dissertation  
Issuance:  monographic  
Date Issued:  2004  
Publisher:  Florida Atlantic University  
Place of Publication:  Boca Raton, Fla.  
Physical Form:  application/pdf  
Extent:  37 p.  
Language(s):  English  
Summary:  We present several results involving three concepts: Prufer domains, the strong 2generator property, and integervalued polynomials. An integral domain D is called a Prufer domain if every nonzero finitely generated ideal of D is invertible. When each 2generated ideal of D has the property that one of its generators can be any arbitrary selected nonzero element of the ideal, we say D has the strong 2generator property . We note that, if D has the strong 2generator property, then D is a Prufer domain. If Q is the field of fractions of D, and E is a finite nonempty subset of D; we define Int(E, D ) = {f(X) ∈ Q[ X] ∣ f(a) ∈ D for every a ∈ E} to be the ring of integervalued polynomials on D with respect to the subset E. We show that D is a Prufer domain if and only if Int(E, D) is a Prufer domain. Our main theorem is that Int(E, D) has the strong 2generator property if and only if D is a Bezout domain (that is, every finitely generated ideal of D is principal).  
Identifier:  9780496257317 (isbn), 13151 (digitool), FADT13151 (IID), fau:10012 (fedora)  
Collection:  FAU Electronic Theses and Dissertations Collection  
Note(s): 
Thesis (M.S.)Florida Atlantic University, 2004. Charles E. Schmidt College of Science 

Subject(s): 
Prüfer rings Rings of integers Polynomials Ideals (Algebra) Mathematical analysis 

Held by:  Florida Atlantic University Libraries  
Persistent Link to This Record:  http://purl.flvc.org/fcla/dt/13151  
Sublocation:  Digital Library  
Use and Reproduction:  Copyright © is held by the author with permission granted to Florida Atlantic University to digitize, archive and distribute this item for nonprofit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.  
Owner Institution:  FAU  
Is Part of Series:  Florida Atlantic University Digital Library Collections. 