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Title

AuslanderReiten theory for systems of submodule embeddings.

Creator

Moore, Audrey., Charles E. Schmidt College of Science, Department of Mathematical Sciences

Abstract/Description

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...
Show moreIn 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.
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Date Issued

2009

PURL

http://purl.flvc.org/fcla/dt/210496

Subject Headings

Artin algebras, Rings (Algebra), Representation of algebras, Embeddings (Mathematics), Linear algebraic groups

Format

Document (PDF)