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Maximally Prüfer rings

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Date Issued:
2015
Summary:
In this dissertation, we consider six Prufer-like conditions on acommutative ring R. These conditions form a hierarchy. Being a Prufer ring is not a local property: a Prufer ring may not remain a Prufer ring when localized at a prime or maximal ideal. We introduce a seventh condition based on this fact and extend the hierarchy. All the conditions of the hierarchy become equivalent in the case of a domain, namely a Prufer domain. We also seek the relationship of the hierarchy with strong Prufer rings.
Title: Maximally Prüfer rings.
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Name(s): Sharma, Madhav, author
Klingler, Lee, Thesis advisor
Florida Atlantic University, Degree grantor
Charles E. Schmidt College of Science
Department of Mathematical Sciences
Type of Resource: text
Genre: Electronic Thesis Or Dissertation
Date Created: 2015
Date Issued: 2015
Publisher: Florida Atlantic University
Place of Publication: Boca Raton, Fla.
Physical Form: application/pdf
Extent: 53 p.
Language(s): English
Summary: In this dissertation, we consider six Prufer-like conditions on acommutative ring R. These conditions form a hierarchy. Being a Prufer ring is not a local property: a Prufer ring may not remain a Prufer ring when localized at a prime or maximal ideal. We introduce a seventh condition based on this fact and extend the hierarchy. All the conditions of the hierarchy become equivalent in the case of a domain, namely a Prufer domain. We also seek the relationship of the hierarchy with strong Prufer rings.
Identifier: FA00004465 (IID)
Degree granted: Dissertation (Ph.D.)--Florida Atlantic University, 2015
Collection: FAU Electronic Theses and Dissertations Collection
Note(s): Includes bibliography.
Subject(s): Approximation theory
Commutative algebra
Commutative rings
Geometry, Algebraic
Ideals (Algebra)
Mathematical analysis
Prüfer rings
Rings (Algebra)
Rings of integers
Held by: Florida Atlantic University Libraries
Sublocation: Digital Library
Links: http://purl.flvc.org/fau/fd/FA00004465
Persistent Link to This Record: http://purl.flvc.org/fau/fd/FA00004465
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Host Institution: FAU
Is Part of Series: Florida Atlantic University Digital Library Collections.