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Ring Extensions Involving Amalgamated Duplications

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dc.contributor.advisor Shapiro, Jay A. Long, Timothy Scott
dc.creator Long, Timothy Scott en_US 2014-09-18T01:56:12Z 2014-09-18T01:56:12Z 2014-05 en_US
dc.description.abstract Within 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.extent 106 pages en_US
dc.language.iso en en_US
dc.rights Copyright 2014 Timothy Scott Long en_US
dc.subject Mathematics en_US
dc.subject Algebra en_US
dc.subject Amalgamated Duplication en_US
dc.subject Bowtie Ring en_US
dc.subject Epimorphism en_US
dc.subject Idealization en_US
dc.subject Ring Extension en_US
dc.title Ring Extensions Involving Amalgamated Duplications en_US
dc.type Dissertation en Doctoral en Mathematics en George Mason University en

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