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

Creative Commons License
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.

Research Data and Supplementary Material

No

Share

COinS