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Almost Dedekind Domains and Atomicity
(North Dakota State University, 2012)
The objective of this dissertation was to determine the class of domains that are both almost Dedekind and atomic. To investigate this question we constructed a global object called the norm, and used it to determine ...
Integral Closure and the Generalized Multiplicity Sequence
(North Dakota State University, 2015)
See Dissertation Document for Full Abstract (Mathematical Symbols Included)
Gorenstein Dimension over Some Rings of the Form R [0 plus]C
(North Dakota State University, 2015)
Commutative algebra is the study of commutative rings and other abstract structures based on commutative rings. Modules can be viewed as a common generalization of several of those structures, and some invariants, e.g. ...
The Half-Factorial Property in Polynomial Rings
(North Dakota State University, 2014)
This dissertation investigates the following question: If R is a half-factorial domain (HFD) and x is an indeterminate, under what conditions is the polynomial ring R[x] an HFD? The question has been answered in a few ...
DG Homological Algebra, Properties of Ring Homomorphisms, and the Generalized Auslander-Reiten Conjecture
(North Dakota State University, 2013)
This dissertation contains three aspects of my research that are listed as three joint papers with my advisor and a solo paper in the bibliography [56]--[59]. Each paper will be discussed in a different chapter. Chapter 1 ...
Mathematical Modeling of Epidemics: Parametric Heterogeneity and Pathogen Coexistence
(North Dakota State University, 2020)
No two species can indefinitely occupy the same ecological niche according to the competitive exclusion principle. When competing strains of the same pathogen invade a homogeneous population, the strain with the largest ...
Knot Groups and Bi-Orderable HNN Extensions of Free Groups
(North Dakota State University, 2020)
Suppose K is a fibered knot with bi-orderable knot group. We perform a topological winding operation to half-twist bands in a free incompressible Seifert surface Σ of K. This results in a Seifert surface Σ' with boundary ...
Codualizing Modules and Complexes
(North Dakota State University, 2013)
See dissertation for full abstract and properly formatted mathematical formulas.
Variational Methods for Polycrystal Plasticity and Related Topics in Partial Differential Equations
(North Dakota State University, 2013)
In the first part of the thesis the effective yield set of ionic polycrystals is characterized by means of variational principles in L∞ that are associated to supremal functionals acting on matrix-valued divergence-free ...
Semidualizing DG Modules over Tensor Products
(North Dakota State University, 2015)
In this dissertation, we study rings: sets with addition, subtraction, and multiplication. One way to study a ring is by studying its modules: the algebraic objects the ring acts on. Since it is impractical to study all ...