Browsing Mathematics Doctoral Work by Issue Date
Now showing items 1-20 of 31
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Ramification and Infinite Extensions of Dedekind Domains
(North Dakota State University, 2010)This dissertation presents methods for determining the behavior of prime ideals m an integral extension of a Dedekind domain. One tool used to determine this behavior is an algorithm that computes which prime ideals ... -
Applications of Groups of Divisibility and a Generalization of Krull Dimension
(North Dakota State University, 2011)Groups of divisibility have played an important role in commutative algebra for many years. In 1932 Wolfgang Krull showed in [12] that every linearly ordered Abelian group can be realized as the group of divisibility of a ... -
Atomicity in Rings with Zero Divisors
(North Dakota State University, 2011)In this dissertation, we examine atomicity in rings with zero divisions. We begin by examining the relationship between a ring’s level of atomicity and the highest level of irreducibility shared by the ring’s irreducible ... -
The Game of Nim on Graphs
(North Dakota State University, 2011)The ordinary game of Nim has a long history and is well-known in the area of combinatorial game theory. The solution to the ordinary game of Nim has been known for many years and lends itself to numerous other solutions ... -
NAK for Ext, Ascent of Module Structures, and the Blindness of Extended Modules
(North Dakota State University, 2012)This dissertation investigates the interplay between properties of Ext modules and ascent of module structures along ring homomorphisms. First, we consider a flat local ring homomorphism ϕ: (R, [special characters omitted], ... -
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 ... -
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 ... -
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 ... -
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 ... -
Ideal Graphs
(North Dakota State University, 2014)In this dissertation, we explore various types of graphs that can be associated to a commutative ring with identity. In particular, if R is a commutative ring with identity, we consider a number of graphs with the vertex ... -
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. ... -
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 ... -
Modeling Swap and Geophysical Analysis using Barndorff-Nielson and Shephard Model
(North Dakota State University, 2015)Video summarizing Ph.D. dissertation for a non-specialist audience. -
L1 Approximation in De Branges Spaces
(North Dakota State University, 2015)In this thesis we study bandlimited approximations to various functions. Bandlimited functions have compactly supported Fourier transforms, which is a desirable feature in many applications. In particular, we address the ... -
Modeling Financial Swaps and Geophysical data Using the Barndorff-Nielsen and Shephard Model
(North Dakota State University, 2015)This dissertation uses Barndoff-Nielsen and Shephard (BN-S) models to model swap, a type of financial derivative, and analyze geophysical data for estimation of major earthquakes. From empirical observation of the stock ... -
Homological Dimensions with Respect to a Semidualizing Complex
(North Dakota State University, 2015)See Dissertation Document for Full Abstract (Mathematical Symbols Included) -
Subfractals Induced by Subshifts
(North Dakota State University, 2016)In this thesis, a subfractal is the subset of points in the attractor of an iterated function system in which every point in the subfractal is associated with an allowable word from a subshift on the underlying symbolic ... -
Optimization Problems Arising in Stability Analysis of Discrete Time Recurrent Neural Networks
(North Dakota State University, 2016)We consider the method of Reduction of Dissipativity Domain to prove global Lyapunov stability of Discrete Time Recurrent Neural Networks. The standard and advanced criteria for Absolute Stability of these essentially ...