Term of Award
Fall 2018
Degree Name
Master of Science in Mathematics (M.S.)
Document Type and Release Option
Thesis (open access)
Copyright Statement / License for Reuse
This work is licensed under a Creative Commons Attribution 4.0 License.
Department
Department of Mathematical Sciences
Committee Chair
Jimmy Dillies
Committee Member 1
Paul Sobaje
Committee Member 2
Alina Iacob
Committee Member 3
Enka Lakuriqi
Abstract
The first idea of this research was to study a topic that is related to both Algebra and Topology and explore a tool that connects them together. That was the entrance for me to the “adic world”. What was needed were some important concepts from Algebra and Topology, and so they are treated in the first two chapters.
The reader is assumed to be familiar with Abstract Algebra and Topology, especially with Ring theory and basics of Point-set Topology.
The thesis consists of a motivation and four chapters, the third and the fourth being the main ones. In the third chapter, we introduce the p-adic numbers and the f-adic rings, while adic spaces are considered in the last chapter.
Adic spaces are relatively new topic in pure mathematics that have seen many devel- opments in the last few years. Their significance enters from the bridging ability that they have to connect Algebra and Geometry, as we can see in the last chapter.
OCLC Number
1085541895
Recommended Citation
Kadhem, Fayadh, "A Journey to the Adic World" (2018). Electronic Theses and Dissertations. 1836.
https://digitalcommons.georgiasouthern.edu/etd/1836
Research Data and Supplementary Material
No
