| dc.contributor.author | Batell, Mark Thomas | |
| dc.description.abstract | This dissertation investigates the following question: If R is a half-factorial domain (HFD) and x is an indeterminate, under what conditions is the polynomial ring R[x] an HFD? The question has been answered in a few special cases. A classical result of Gauss states that if R is a UFD, then R[x] is a UFD. Also, Zaks showed that if R is a Krull domain with class group Cl(R), then R[x] is an HFD if and only if jCl(R)j 6 2. In the proof of his result, Zaks did not use Gauss's methods. We give a new proof that does. We also study the question in domains other than Krull domains. | en_US |
| dc.publisher | North Dakota State University | en_US |
| dc.rights | NDSU Policy 190.6.2 | |
| dc.title | The Half-Factorial Property in Polynomial Rings | en_US |
| dc.type | Dissertation | en_US |
| dc.date.accessioned | 2018-01-24T15:22:13Z | |
| dc.date.available | 2018-01-24T15:22:13Z | |
| dc.date.issued | 2014 | |
| dc.identifier.uri | https://hdl.handle.net/10365/27311 | |
| dc.rights.uri | https://www.ndsu.edu/fileadmin/policy/190.pdf | |
| ndsu.degree | Doctor of Philosophy (PhD) | en_US |
| ndsu.college | Science and Mathematics | en_US |
| ndsu.department | Mathematics | en_US |
| ndsu.program | Mathematics | en_US |
| ndsu.advisor | Coykendall, Jim | |
| ndsu.advisor | Duncan, Benton | |
