Mixed modules and endomorphisms over incomplete discrete valuation rings.

Persistent Link:
http://hdl.handle.net/10150/186189
Title:
Mixed modules and endomorphisms over incomplete discrete valuation rings.
Author:
Files, Steve Todd.
Issue Date:
1993
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:
Structure theorems are given for several classes of mixed modules over an arbitrary discrete valuation ring R, followed by results on the endomorphism algebras of mixed R-modules. The opening chapter introduces a fundamental embedding of R-modules into related modules over the p-adic completion of R, and the succeeding two chapters develop generalizations of the theory of simply presented modules of rank one and Warfield modules. Endomorphism algebras are considered in the penultimate chapter, where it is shown that the related modules over the completion of R are isomorphic if the underlying R-modules possess isomorphic endomorphism algebras. An isomorphism theorem for the endomorphism algebras of Warfield modules is deduced. Relevant constructions of mixed abelian groups are offered in the final chapter.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Dissertations, Academic.; Mathematics.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Mathematics; Graduate College
Degree Grantor:
University of Arizona
Committee Chair:
May, Warren

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleMixed modules and endomorphisms over incomplete discrete valuation rings.en_US
dc.creatorFiles, Steve Todd.en_US
dc.contributor.authorFiles, Steve Todd.en_US
dc.date.issued1993en_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.abstractStructure theorems are given for several classes of mixed modules over an arbitrary discrete valuation ring R, followed by results on the endomorphism algebras of mixed R-modules. The opening chapter introduces a fundamental embedding of R-modules into related modules over the p-adic completion of R, and the succeeding two chapters develop generalizations of the theory of simply presented modules of rank one and Warfield modules. Endomorphism algebras are considered in the penultimate chapter, where it is shown that the related modules over the completion of R are isomorphic if the underlying R-modules possess isomorphic endomorphism algebras. An isomorphism theorem for the endomorphism algebras of Warfield modules is deduced. Relevant constructions of mixed abelian groups are offered in the final chapter.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectDissertations, Academic.en_US
dc.subjectMathematics.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.chairMay, Warrenen_US
dc.contributor.committeememberToubassi, Eliasen_US
dc.contributor.committeememberGrove, Larryen_US
dc.identifier.proquest9322690en_US
dc.identifier.oclc715421706en_US
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