Current Search: Moore, Audrey. (x)
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Title
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Auslander-Reiten theory for systems of submodule embeddings.
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Creator
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Moore, Audrey., Charles E. Schmidt College of Science, Department of Mathematical Sciences
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Abstract/Description
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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...
Show moreIn 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.
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Date Issued
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2009
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PURL
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http://purl.flvc.org/fcla/dt/210496
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Subject Headings
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Artin algebras, Rings (Algebra), Representation of algebras, Embeddings (Mathematics), Linear algebraic groups
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Format
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Document (PDF)
