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Rings of integer-valued polynomials and derivatives
| Title: | Rings of integer-valued polynomials and derivatives. |
 129 views 13 downloads |
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| Name(s): |
Villanueva, Yuri. Charles E. Schmidt College of Science Department of Mathematical Sciences |
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| 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 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. | |
| 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. |
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| Subject(s): |
Rings of integers Ideals (Algebra) Polynomials Arithmetic algebraic geometry Categories (Mathematics) Commutative algebra |
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| Persistent Link to This Record: | http://purl.flvc.org/FAU/3356899 | |
| Use and Reproduction: | http://rightsstatements.org/vocab/InC/1.0/ | |
| Host Institution: | FAU |
