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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 

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Persistent Link to This Record:  http://purl.flvc.org/fcla/dt/13151  
Sublocation:  Digital Library  
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Owner Institution:  FAU  
Is Part of Series:  Florida Atlantic University Digital Library Collections. 