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Minimal zerodimensional extensions
 Date Issued:
 2009
 Summary:
 The structure of minimal zerodimensional extension of rings with Noetherian spectrum in which zero is a primary ideal and with at most one prime ideal of height greater than one is determined. These rings include K[[X,T]] where K is a field and Dedenkind domains, but need not be Noetherian nor integrally closed. We show that for such a ring R there is a onetoone correspondence between isomorphism classes of minimal zerodimensional extensions of R and sets M, where the elements of M are ideals of R primary for distinct prime ideals of height greater than zero. A subsidiary result is the classification of minimal zerodimensional extensions of general ZPIrings.
Title:  Minimal zerodimensional extensions. 
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Name(s): 
Chiorescu, Marcela Florida Atlantic University Charles E. Schmidt College of Science Department of Mathematical Sciences 

Type of Resource:  text  
Genre:  Electronic Thesis Or Dissertation  
Date Issued:  2009  
Publisher:  Florida Atlantic University  
Physical Form:  electronic  
Extent:  v, 43 p. : ill.  
Language(s):  English  
Summary:  The structure of minimal zerodimensional extension of rings with Noetherian spectrum in which zero is a primary ideal and with at most one prime ideal of height greater than one is determined. These rings include K[[X,T]] where K is a field and Dedenkind domains, but need not be Noetherian nor integrally closed. We show that for such a ring R there is a onetoone correspondence between isomorphism classes of minimal zerodimensional extensions of R and sets M, where the elements of M are ideals of R primary for distinct prime ideals of height greater than zero. A subsidiary result is the classification of minimal zerodimensional extensions of general ZPIrings.  
Identifier:  417653151 (oclc), 210447 (digitool), FADT210447 (IID), fau:3405 (fedora)  
Note(s): 
by Marcela Chiorescu. Thesis (Ph.D.)Florida Atlantic University, 2009. Includes bibliography. Electronic reproduction. Boca Raton, Fla., 2009. Mode of access: World Wide Web. 

Subject(s): 
Algebra, Abstract Noetherian rings Commutative rings Modules (Algebra) Algebraic number theory 

Persistent Link to This Record:  http://purl.flvc.org/FAU/210447  
Use and Reproduction:  http://rightsstatements.org/vocab/InC/1.0/  
Host Institution:  FAU 