Persistent Link:
http://hdl.handle.net/10150/282294
Title:
Endomorphisms of modules over discrete valuation domains
Author:
Cheng, Yu-Wen, 1961-
Issue Date:
1997
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
The primary objective of this dissertation is to study isomorphism theorems (or isomorphism problems) for modules over either complete or non-complete discrete valuation domains. The first chapter of the dissertation lays the foundation for all the remaining chapters. We first review the definition and some important facts about modules over discrete valuation domains. p-adic topologies and the notion of complete modules are then introduced, and indecomposable modules are examined. Then, we list some facts on homomorphism algebras of modules over discrete valuation domains that are necessary for our later studies. In the second chapter, we consider all possible isomorphism problems of modules over a complete discrete valuation domain. Kaplansky's and Wolfson's Theorems are presented, and we show that the isomorphism problem of modules over complete discrete valuation domains can be reduced to the isomorphism problem of reduced modules M with M/tM divisible. Finally, in the last chapter, we study isomorphism theorems for modules over a general discrete valuation domain. We present an isomorphism theorem for a special class of modules over a discrete valuation domain such that if M is in the class then any isomorphism of EndR(M) and EndR is induced by an isomorphism of M with M*
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Mathematics.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Mathematics
Degree Grantor:
University of Arizona
Advisor:
Way, Warren

Full metadata record

DC FieldValue Language
dc.language.isoen_USen_US
dc.titleEndomorphisms of modules over discrete valuation domainsen_US
dc.creatorCheng, Yu-Wen, 1961-en_US
dc.contributor.authorCheng, Yu-Wen, 1961-en_US
dc.date.issued1997en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractThe primary objective of this dissertation is to study isomorphism theorems (or isomorphism problems) for modules over either complete or non-complete discrete valuation domains. The first chapter of the dissertation lays the foundation for all the remaining chapters. We first review the definition and some important facts about modules over discrete valuation domains. p-adic topologies and the notion of complete modules are then introduced, and indecomposable modules are examined. Then, we list some facts on homomorphism algebras of modules over discrete valuation domains that are necessary for our later studies. In the second chapter, we consider all possible isomorphism problems of modules over a complete discrete valuation domain. Kaplansky's and Wolfson's Theorems are presented, and we show that the isomorphism problem of modules over complete discrete valuation domains can be reduced to the isomorphism problem of reduced modules M with M/tM divisible. Finally, in the last chapter, we study isomorphism theorems for modules over a general discrete valuation domain. We present an isomorphism theorem for a special class of modules over a discrete valuation domain such that if M is in the class then any isomorphism of EndR(M) and EndR is induced by an isomorphism of M with M*en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectMathematics.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorWay, Warrenen_US
dc.identifier.proquest9729429en_US
dc.identifier.bibrecord.b34775870en_US
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