Document Type
Thesis
Date of Award
2023
Degree Name
Master of Science (MS)
Department
Mathematics
First Advisor
Ramiro Lafuente-Rodriguez
Abstract
The primary purpose of this thesis is to construct a topology on the collection of maximal ideals of a distributive and complemented lattice using the hull-kernel methodology. Through the construction of this topological space, we discovered that the space is compact, zero-dimensional, and Hausdorff. Next, we looked at the properties of some lattices, namely the power set of a finite set ordered by inclusion and the set of all positives divisors for some arbitrary integer ordered by divisibility. Whenever these lattices were both distributive and complemented, we constructed a topology on the collection of maximal ideals of the lattices using the hull-kernel methodology. Finally, we applied our prior results to these topological spaces to help us further understand the structure of a topological space constructed using this methodology.
Subject Categories
Mathematics
Keywords
Boolean algebra, lattice, order theory, poset
Number of Pages
59
Publisher
University of South Dakota
Recommended Citation
Moos, Abbigal, "Explorations of a Topology Constructed on the Maximal Ideals of a Boolean Algebra" (2023). Dissertations and Theses. 130.
https://red.library.usd.edu/diss-thesis/130