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prime spectrum of a ring: A survey
 Date Issued:
 1991
 Summary:
 This thesis has as its motivation the exploration, on an informal level, of a correspondence between Algebra and Topology. Specifically, it considers the prime spectrum of a ring, that is, the set of prime ideals, endowed with the Zariski topology. Questions posed by M. Atiyah and I. MacDonald in their book, "Introduction to Commutative Algebra", serve as a guideline through most of this work. The final section, however, follows R. Heitmann's paper, "Generating NonNoetherian Modules Efficiently". This section examines the patch topology on the prime spectrum of a ring where the patch topology has as a closed subbasis the Zariski closed and Zariski quasicompact open sets. It is proven that the prime spectrum of a ring with the patch topology is a compact Hausdorff space, and several relationships between the patch and Zariski topologies are established. The final section concludes with a technical theorem having a number of interesting corollaries, among which are a stable range theorem and a theorem of Kronecker, both generalized to the nonNoetherian setting.
Title:  The prime spectrum of a ring: A survey. 
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Name(s): 
Fernandez, James Stephen Florida Atlantic University, Degree Grantor Klingler, Lee, Thesis Advisor 

Type of Resource:  text  
Genre:  Electronic Thesis Or Dissertation  
Issuance:  monographic  
Date Issued:  1991  
Publisher:  Florida Atlantic University  
Place of Publication:  Boca Raton, Fla.  
Physical Form:  application/pdf  
Extent:  60 p.  
Language(s):  English  
Summary:  This thesis has as its motivation the exploration, on an informal level, of a correspondence between Algebra and Topology. Specifically, it considers the prime spectrum of a ring, that is, the set of prime ideals, endowed with the Zariski topology. Questions posed by M. Atiyah and I. MacDonald in their book, "Introduction to Commutative Algebra", serve as a guideline through most of this work. The final section, however, follows R. Heitmann's paper, "Generating NonNoetherian Modules Efficiently". This section examines the patch topology on the prime spectrum of a ring where the patch topology has as a closed subbasis the Zariski closed and Zariski quasicompact open sets. It is proven that the prime spectrum of a ring with the patch topology is a compact Hausdorff space, and several relationships between the patch and Zariski topologies are established. The final section concludes with a technical theorem having a number of interesting corollaries, among which are a stable range theorem and a theorem of Kronecker, both generalized to the nonNoetherian setting.  
Identifier:  14763 (digitool), FADT14763 (IID), fau:11554 (fedora)  
Note(s):  Thesis (M.S.)Florida Atlantic University, 1991.  
Subject(s):  Rings (Algebra)  
Held by:  Florida Atlantic University Libraries  
Persistent Link to This Record:  http://purl.flvc.org/fcla/dt/14763  
Sublocation:  Digital Library  
Use and Reproduction:  Copyright © is held by the author with permission granted to Florida Atlantic University to digitize, archive and distribute this item for nonprofit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.  
Use and Reproduction:  http://rightsstatements.org/vocab/InC/1.0/  
Host Institution:  FAU  
Is Part of Series:  Florida Atlantic University Digital Library Collections. 