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The Global ETD Search service is a free service for researchers
to find electronic theses and dissertations. This service is
provided by the
Networked Digital Library of Theses and Dissertations.
Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
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Finite Generation of Ext-Algebras for Monomial AlgebrasCone, Randall Edward 09 December 2010 (has links)
The use of graphs in algebraic studies is ubiquitous, whether the graphs be finite or infinite, directed or undirected. Green and Zacharia have characterized finite generation of the cohomology rings of monomial algebras, and thereafter G. Davis determined a finite criteria for such generation in the case of cycle algebras. Herein, we describe the construction of a finite directed graph upon which criteria can be established to determine finite generation of the cohomology ring of in-spoked cycle" algebras, a class of algebras that includes cycle algebras. We then show the further usefulness of this constructed graph by studying other monomial algebras, including d-Koszul monomial algebras and a new class of monomial algebras which we term "left/right-symmetric" algebras. / Ph. D.
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Dehn's Problems And Geometric Group TheoryLaBrie, Noelle 01 June 2024 (has links) (PDF)
In 1911, mathematician Max Dehn posed three decision problems for finitely
presented groups that have remained central to the study of combinatorial
group theory. His work provided the foundation for geometric group theory,
which aims to analyze groups using the topological and geometric properties
of the spaces they act on. In this thesis, we study group actions on Cayley
graphs and the Farey tree. We prove that a group has a solvable word problem
if and only if its associated Cayley graph is constructible. Moreover, we prove
that a group is finitely generated if and only if it acts geometrically on a proper
path-connected metric space. As an example, we show that SL(2, Z) is finitely
generated by proving that it acts geometrically on the Farey tree.
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Reduktionssysteme zur Berechnung einer Auflösung der orthogonalen freien Quantengruppen A<sub>o</sub>(n) / Reduction systems for computing a resolution of the free orthogonal quantum groups A<sub>o</sub>(n)Härtel, Johannes 04 July 2008 (has links)
No description available.
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