Ring Extensions Involving Amalgamated Duplications

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dc.contributor.advisorShapiro, Jay A.
dc.contributor.authorLong, Timothy Scott
dc.creatorLong, Timothy Scott
dc.date.accessioned2014-09-18T01:56:12Z
dc.date.available2014-09-18T01:56:12Z
dc.date.issued2014-05
dc.description.abstractWithin the last decade, much attention in commutative ring theory has been drawn into the revitalized concept of an “amalgamated duplication of a ring along an ideal,” also known simply as a “bowtie ring.” The basic bowtie ring construction has roots as early as 1932, while the updated form simultaneously generalizes myriad other known constructions, including D + M rings, A + B rings, the rings A + B[X] and A + B[[X]] (for an extension ring B of the ring A), and Nagata's idealization of a module, a concept which itself has been indispensable in commutative algebra for over 50 years in providing examples of non-domains with various desired properties.
dc.format.extent106 pages
dc.identifier.urihttps://hdl.handle.net/1920/8896
dc.language.isoen
dc.rightsCopyright 2014 Timothy Scott Long
dc.subjectMathematics
dc.subjectAlgebra
dc.subjectAmalgamated Duplication
dc.subjectBowtie Ring
dc.subjectEpimorphism
dc.subjectIdealization
dc.subjectRing Extension
dc.titleRing Extensions Involving Amalgamated Duplications
dc.typeDissertation
thesis.degree.disciplineMathematics
thesis.degree.grantorGeorge Mason University
thesis.degree.levelDoctoral

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