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Auslander-Reiten theory for systems of submodule embeddings
- Date Issued:
- 2009
- Summary:
- In this dissertation, we will investigate aspects of Auslander-Reiten theory adapted to the setting of systems of submodule embeddings. Using this theory, we can compute Auslander-Reiten 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 Ringel-Tachikawa Theorem which states that for an artinian ring R of finite representation type, each R-module is a direct sum of finite-length indecomposable R-modules. In cases where this applies, the indecomposable objects obtained in the Auslander-Reiten 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 Calabi-Yau dimension of such a category.
Title: | Auslander-Reiten theory for systems of submodule embeddings. |
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Name(s): |
Moore, Audrey. Charles E. Schmidt College of Science Department of Mathematical Sciences |
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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 Auslander-Reiten theory adapted to the setting of systems of submodule embeddings. Using this theory, we can compute Auslander-Reiten 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 Ringel-Tachikawa Theorem which states that for an artinian ring R of finite representation type, each R-module is a direct sum of finite-length indecomposable R-modules. In cases where this applies, the indecomposable objects obtained in the Auslander-Reiten 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 Calabi-Yau 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. |
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Subject(s): |
Artin algebras Rings (Algebra) Representation of algebras Embeddings (Mathematics) Linear algebraic groups |
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Persistent Link to This Record: | http://purl.flvc.org/fcla/dt/210496 | |
Use and Reproduction: | http://rightsstatements.org/vocab/InC/1.0/ | |
Host Institution: | FAU |