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AuslanderReiten theory for systems of submodule embeddings
 Date Issued:
 2009
 Summary:
 In this dissertation, we will investigate aspects of AuslanderReiten theory adapted to the setting of systems of submodule embeddings. Using this theory, we can compute AuslanderReiten quivers of such categories, which among other information, yields valuable information about the indecomposable objects in such a category. A main result of the dissertation is an adaptation to this situation of the Auslander and RingelTachikawa Theorem which states that for an artinian ring R of finite representation type, each Rmodule is a direct sum of finitelength indecomposable Rmodules. In cases where this applies, the indecomposable objects obtained in the AuslanderReiten quiver give the building blocks for the objects in the category. We also briefly discuss in which cases systems of submodule embeddings form a Frobenius category, and for a few examples explore pointwise CalabiYau dimension of such a category.
Title:  AuslanderReiten theory for systems of submodule embeddings. 
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Name(s): 
Moore, Audrey. 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:  xi, 112 p. : ill.  
Language(s):  English  
Summary:  In this dissertation, we will investigate aspects of AuslanderReiten theory adapted to the setting of systems of submodule embeddings. Using this theory, we can compute AuslanderReiten quivers of such categories, which among other information, yields valuable information about the indecomposable objects in such a category. A main result of the dissertation is an adaptation to this situation of the Auslander and RingelTachikawa Theorem which states that for an artinian ring R of finite representation type, each Rmodule is a direct sum of finitelength indecomposable Rmodules. In cases where this applies, the indecomposable objects obtained in the AuslanderReiten quiver give the building blocks for the objects in the category. We also briefly discuss in which cases systems of submodule embeddings form a Frobenius category, and for a few examples explore pointwise CalabiYau dimension of such a category.  
Identifier:  422624278 (oclc), 210496 (digitool), FADT210496 (IID), fau:3409 (fedora)  
Note(s): 
by Audrey Moore. Thesis (Ph.D.)Florida Atlantic University, 2009. Includes bibliography. Electronic reproduction. Boca Raton, Fla., 2009. Mode of access: World Wide Web. 

Subject(s): 
Artin algebras Rings (Algebra) Representation of algebras Embeddings (Mathematics) Linear algebraic groups 

Persistent Link to This Record:  http://purl.flvc.org/fcla/dt/210496  
Use and Reproduction:  http://rightsstatements.org/vocab/InC/1.0/  
Owner Institution:  FAU 