The objective of this dissertation was to determine the class of domains that are both almost Dedekind and atomic. To investigate this question we constructed a global object called the norm, and used it to determine properties that a domain must have to be both atomic and almost Dedekind. Additionally we use topological notions on the spectrum of a domain to determine atomicity. We state some theorems with regard to ACCP and class groups. The lemmas and theorems in this dissertation answer in part the objective. We conclude with a chapter of future study that aims to approach a complete answer to the objective.
| Identifer | oai:union.ndltd.org:ndsu.edu/oai:library.ndsu.edu:10365/26692 |
| Date | January 2012 |
| Creators | Hasenauer, Richard Erwin |
| Publisher | North Dakota State University |
| Source Sets | North Dakota State University |
| Detected Language | English |
| Type | text/dissertation |
| Format | application/pdf |
| Rights | NDSU Policy 190.6.2, https://www.ndsu.edu/fileadmin/policy/190.pdf |
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