Author | Kardos, Michael | |
Date Accessioned | 2023-06-05T13:54:47Z | |
Date Available | 2023-06-05T13:54:47Z | |
Date Created | 2023-05 | |
Date of Issue | 2023-05-03 | |
xmlui.metadata.dc.date.submitted | May 2023 | |
Identifier (URI) | http://hdl.handle.net/10342/12855 | |
Description | We discuss the technical background and relevant research regarding the undecidability of $O_{\mathbb{Q}^{\text{ab}}}$. Given an algebraic extension $K/\mathbb{Q}$, we consider the subring defined by
$$R_K=\{x\in O_K\,|\,\forall \varepsilon\in U_K\setminus\{1\}\,\exists\delta\in U_K:\delta-1\equiv x(\varepsilon-1)\bmod(\varepsilon-1)^2\}.$$
We later consider a similar construction over subrings of $\mathbb{Q}$ of characteristic $0$. In doing this, we hope to gain insight into the result of the construction of $R_K$ when $K=\mathbb{Q}^{\text{ab}}$. | |
Mimetype | application/pdf | |
Language | en | |
Publisher | East Carolina University | |
Subject | number theory | |
Subject | logic | |
Subject | subring | |
Subject | abelian | |
Subject | extension | |
Subject | unit | |
Subject | definability | |
Title | First Order Definition of Rings Using Group of Units | |
Type | Master's Thesis | |
xmlui.metadata.dc.date.updated | 2023-06-02T15:41:00Z | |
Department | Mathematics | |
xmlui.metadata.dc.degree.name | M.A. | |
xmlui.metadata.dc.degree.level | Masters | |
xmlui.metadata.dc.degree.discipline | MA-Mathematics | |
xmlui.metadata.dc.degree.grantor | East Carolina University | |
xmlui.metadata.dc.degree.department | Mathematics | |
xmlui.metadata.dc.type.material | text | |