| dc.contributor.author | Hashbarger, Carl Stanley | |
| dc.description.abstract | This dissertation presents methods for determining the behavior of prime ideals
m an integral extension of a Dedekind domain. One tool used to determine this
behavior is an algorithm that computes which prime ideals ramify in a finite separable
extension. Other results about factorization of prime ideals are improved and applied
to finite extensions. By considering a set of finite extensions whose union is an infinite
extension, it is possible to predict ideal factorization in the infinite extension as
well. Among other things, this ideal factorization determines whether a given infinite
extension is almost Dedekind. These methods and results yield some interesting facts
when they are demonstrated on a pair of classical rings of algebraic number theory. | en_US |
| dc.publisher | North Dakota State University | en_US |
| dc.rights | NDSU policy 190.6.2 | en_US |
| dc.title | Ramification and Infinite Extensions of Dedekind Domains | en_US |
| dc.type | Dissertation | en_US |
| dc.date.accessioned | 2024-03-07T21:47:18Z | |
| dc.date.available | 2024-03-07T21:47:18Z | |
| dc.date.issued | 2010 | |
| dc.identifier.uri | https://hdl.handle.net/10365/33716 | |
| dc.subject.lcsh | Dedekind rings. | en_US |
| dc.subject.lcsh | Integral domains. | en_US |
| dc.subject.lcsh | Algebraic number theory. | en_US |
| dc.rights.uri | https://www.ndsu.edu/fileadmin/policy/190.pdf | en_US |
| 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, James | |
