Browsing by Author "Albrecht, Ulrich"

Now showing items 1-10 of 10

Dedekind Domains and the P-rank of Ext

James, Daniel (2017-04-21)

We address what can be said of torsion-free finite rank modules $A$ and $B$ over a Dedekind domain $R$ when their Ext's are isomorphic, extending an answer to Fuchs' Problem 43 and its dual by Goeters. We obtain a result ...

An Exploratory Study of the Impact of Situated Professional Development for Integrating Technology in Mathematics Instruction on Pedagogical Beliefs and Teaching Practices of Secondary Mathematics Teachers in a School with a High African American, Low-Income Student Population

Ellis, Ruby (2018-12-03)

The purpose of this study was to explore the impact of providing secondary mathematics teachers in a school with a high African American, low-income student population with situated professional development that focuses ...

Finitely Generated Modules Over Noncommutative Chain Rings

Scible, Greggory (2011-10-26)

The notion of a right chain ring, a ring whose lattice of right ideals is linearly ordered by inclusion, is a generalization of a valuation ring. In this work we investigate properties of right chain rings and the structure ...

Morita-Equivalence Between Strongly Non-Singular Rings and the Structure of the Maximal Ring of Quotients

McQuaig, Bradley (2017-07-22)

This dissertation focuses on extending certain notions from Abelian group theory and module theory over integral domains to modules over non-commutative rings. In particular, we investigate generalizations of torsion-freeness ...

Number Fields

Phillips, Gabriel (2017-04-13)

This paper focuses on number fields and the number rings associated with a particular number field. This topic falls under the study of algebra, and in particular algebraic number theory. The motivation of this paper is ...

On Chain and Duo Rings

Santillan-Covarrubias, Francisco Javier (2018-07-26)

The aim of this work is to study a variety of concepts in a non-commutative setting, which originally arose in Commutative Ring Theory. The discussion focuses particularly on properties like hopficity and co-hopficity, ...

On the Growth of Polynomials and Entire Functions of Exponential Type

Harden, Lisa (2004-12-15)

Concerning the growth of a polynomial and its derivative, the following inequalities are well known as Bernstein Inequalities. max(|z|=R) |p(z)| <= max(|z|=1) |p(z)|R^n, for R >= 1, (1) max(|z|=1) |p0(z)| <= max(|z|=1) ...

Products of positive definite symplectic matrices

Granario, Daryl Quebrar (2020-07-15)

We show that every symplectic matrix is a product of five positive definite symplectic matrices and five is the best in the sense that there are symplectic matrices which are not product of less.

Progress on the Marcus-de Oliveira Determinantal Conjecture

Homadi, Khadejah (2017-04-12)

We discuss the well known conjecture of Marcus and de Oliveira of the determinant of the sum of normal matrices. We present the motivation of this conjecture, along with detailed history of its origin. Then we compile ...

Supporting the Development of Teachers' Attributes Needed for the Selection and Implementation of Cognitively Demanding Tasks through Engagement with the MathTwitterBlogosphere

Parrish, Christopher (2016-08-01)

The purpose of this study was to determine if and how engagement with an online community supports the development of three attributes identified by Wilhelm (2014) that teachers need to have in order to consistently select ...