First Order Definition of Rings Using Group of Units
Author
Kardos, Michael
Abstract
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 $K=\mathbb{Q}^{\text{ab}}$.
Subject
Date
2023-05-03
Citation:
APA:
Kardos, Michael.
(May 2023).
First Order Definition of Rings Using Group of Units
(Master's Thesis, East Carolina University). Retrieved from the Scholarship.
(http://hdl.handle.net/10342/12855.)
MLA:
Kardos, Michael.
First Order Definition of Rings Using Group of Units.
Master's Thesis. East Carolina University,
May 2023. The Scholarship.
http://hdl.handle.net/10342/12855.
April 28, 2024.
Chicago:
Kardos, Michael,
“First Order Definition of Rings Using Group of Units”
(Master's Thesis., East Carolina University,
May 2023).
AMA:
Kardos, Michael.
First Order Definition of Rings Using Group of Units
[Master's Thesis]. Greenville, NC: East Carolina University;
May 2023.
Collections
Publisher
East Carolina University