Date of Award
2004
Document Type
Thesis
Publication Status
Version of Record
Submission Date
October 2026
Thesis/Dissertation Advisor [Chair]
Klingler, Lee
Abstract
We present several results involving three concepts: Prufer domains, the strong 2-generator property, and integer-valued polynomials. An integral domain D is called a Prufer domain if every nonzero finitely generated ideal of D is invertible. When each 2-generated 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 2-generator property . We note that, if D has the strong 2-generator 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 integer-valued 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 2-generator property if and only if D is a Bezout domain (that is, every finitely generated ideal of D is principal).
Extent
37 p.
Recommended Citation
Roth, Heather., "Pruefer domains, the strong 2-generator property, and integer-valued polynomials" (2004). Electronic Theses and Dissertations 2000 - 2009. 765.
https://digitalcommons.fau.edu/etd_general_5/765
Identifier
FADT13151
Comments
FAU Electronic Theses and Dissertations Collection|Thesis (M.S.)--Florida Atlantic University, 2004.|Charles E. Schmidt College of Science|FAU Electronic Theses and Dissertations Collection