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Restoring Factorization in Integral DomainsKirk, Susan 01 January 2015 (has links)
This is an expository thesis on integral domains which are not unique factorization domains. We focus on restoring a type of unique factorization using prime ideals within quadratic integer rings. In particular, we examine which quadratic integer rings will admit such factorization.
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Overrings of an Integral DomainEmerson, Sharon Sue 08 1900 (has links)
This dissertation focuses on the properties of a domain which has the property that each ideal is a finite intersection of a π-ideal, the properties of a domain which have the property that each ideal is a finite product of π-ideal, and the containment relations of the resulting classes of ideals. Chapter 1 states definitions which are needed in later chapters. Chapters 2 and 3 focuses on domains which have the property that each ideal in D is a finite intersection of π-ideals while Chapter 4 focuses on domains with the property that each ideal is a finite product of π-ideals. Chapter 5 discusses the containment relations which occur as a result of Chapters 2 and 3.
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A novel finite element discretization of domains with spheroidal geometryTuncer, Necibe. Meir, Amnon J. January 2007 (has links) (PDF)
Dissertation (Ph.D.)--Auburn University, 2007. / Abstract. Includes bibliographic references (p.58-59).
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Torsionless modules and minimal generating sets for ideals of integral domainsBrown, Wesley R., Goeters, Herman Pat. January 2006 (has links) (PDF)
Thesis(M.S.)--Auburn University, 2006. / Abstract. Vita. Includes bibliographic references (p.25).
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Atomicity in Rings with Zero DivisorsTrentham, Stacy Michelle January 2011 (has links)
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 elements. Later, we chose one of the higher forms of atomicity and identify ways of building large classes of examples of rings that rise to this level of atomicity but no higher. Characteristics of the various types of irreducible elements will also be examined. Next, we extend our view to include polynomial extensions of rings with zero divisors. In particular, we focus on properties of the three forms of maximal common divisors and how a ring’s classification as an MCD, SMCD, or VSMCD ring affects its atomicity. To conclude, we identify some unsolved problems relating to the topics discussed in this dissertation.
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