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. / by Yuri Villanueva. / Thesis (Ph.D.)--Florida Atlantic University, 2012. / Includes bibliography. / Mode of access: World Wide Web. / System requirements: Adobe Reader.
| Identifer | oai:union.ndltd.org:fau.edu/oai:fau.digital.flvc.org:fau_3995 |
| Contributors | Villanueva, Yuri., Charles E. Schmidt College of Science, Department of Mathematical Sciences |
| Publisher | Florida Atlantic University |
| Source Sets | Florida Atlantic University |
| Language | English |
| Detected Language | English |
| Type | Text, Electronic Thesis or Dissertation |
| Format | v, 43 p., electronic |
| Rights | http://rightsstatements.org/vocab/InC/1.0/ |
Page generated in 0.0024 seconds