Open Access. Powered by Scholars. Published by Universities.®

Digital Commons Network

Open Access. Powered by Scholars. Published by Universities.®

Mathematics

California State University, San Bernardino

Theses/Dissertations

Rings (Algebra)

Articles 1 - 7 of 7

Full-Text Articles in Entire DC Network

Closure Operations In Commutative Rings, Chloette Joy Samsam Jan 2012

Closure Operations In Commutative Rings, Chloette Joy Samsam

Theses Digitization Project

The purpose of this study is to survey different types of closures and closure operations on commutative rings and ideals.


A Study On The Modular Structures Of Z₂S₃ And Z₅S₃, Bethany Michelle Tasaka Jan 2011

A Study On The Modular Structures Of Z₂S₃ And Z₅S₃, Bethany Michelle Tasaka

Theses Digitization Project

This project is a study of the properties of the modules Z₂S₃ and Z₅S₃, which are examined both as modules over themselves and as modules over their respective integer fields. Each module is examined separately since they each hold distinct properties. The overall goal is to determine the simplicity and semisimplicity of each module.


An Investigation Of Kurosh's Theorem, Keith Anthony Earl Jan 2010

An Investigation Of Kurosh's Theorem, Keith Anthony Earl

Theses Digitization Project

The purpose of this project will be an exposition of the Kurosh Theorem and the necessary and suffcient condition that A must be algebraic and satisfy a P.I. to be locally finite.


Studies In Free Module And It's Basis, Hsu-Chia Chen Jan 2008

Studies In Free Module And It's Basis, Hsu-Chia Chen

Theses Digitization Project

The purpose of this project was to study some basic properties of free modules over a ring. A module with a basis is called a free module and a free module over a division ring (or field) is called a vector space. We show every vector has a basis and any two bases of a vector space have same cardinality. However, a free module over an arbitrary ring (with identity) does not have this property.


Primary Decomposition Of Ideals In A Ring, Sola Oyinsan Jan 2007

Primary Decomposition Of Ideals In A Ring, Sola Oyinsan

Theses Digitization Project

The concept of unique factorization was first recognized in the 1840s, but even then, it was still fairly believed to be automatic. The error of this assumption was exposed largely through attempts to prove Pierre de Fermat's, 1601-1665, last theorem. Once mathematicians discovered that this property did not always hold, it was only natural for them to try to search for the strongest available alternative. Thus began the attempt to generalize unique factorization. Using the ascending chain condition on principle ideals, we will show the conditions under which a ring is a unique factorization domain.


Numbers Of Generators Of Ideals In Local Rings And A Generalized Pascal's Triangle, Lucia Riderer Jan 2005

Numbers Of Generators Of Ideals In Local Rings And A Generalized Pascal's Triangle, Lucia Riderer

Theses Digitization Project

This paper defines generalized binomial coefficients and shows that they can be used to generate generalized Pascal's Triangles and have properties analogous to binomial coefficients. It uses the generalized binomial coefficients to compute the Dilworth number and the Sperner number of certain rings.


Characterizing The Strong Two-Generators Of Certain Noetherian Domains, Ellen Yvonne Green Jan 1997

Characterizing The Strong Two-Generators Of Certain Noetherian Domains, Ellen Yvonne Green

Theses Digitization Project

No abstract provided.