Date of Award
2009
Document Type
Thesis
Publication Status
Version of Record
Submission Date
October 2026
Abstract
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.
Extent
xi, 112 p. : ill.
Recommended Citation
Moore, Audrey., "Auslander-Reiten theory for systems of submodule embeddings" (2009). Electronic Theses and Dissertations 2000 - 2009. 1619.
https://digitalcommons.fau.edu/etd_general_5/1619
Identifier
FADT210496
Comments
by Audrey Moore.|Thesis (Ph.D.)--Florida Atlantic University, 2009.|Includes bibliography.|Electronic reproduction. Boca Raton, Fla., 2009. Mode of access: World Wide Web.|by Audrey Moore.