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Download fileLattices of ideals in graph algebras: refining the join operation
thesis
posted on 2022-04-29, 04:12 authored by McDougall, PhoebeWe consider the ideal structure of Leavitt path algebras of graphs that satisfy Condition (K) over commutative rings with identity. The approach we use takes advantage of the relationship between Leavitt path algebras and Steinberg algebras of boundary path groupoids. We establish a lattice $\mathcal{F}'$ consisting of particular maps $\tau:E^0\to \LR$ and show that this lattice is isomorphic to the lattice of ideals of $L_R(E)$. The advantage to our approach over previous lattice isomorphisms, even in the case that $R$ is a field, is that we obtain convenient join and meet operations in $\mathcal{F}'$. Lastly, we provide three concrete examples.
History
Copyright Date
2022-04-29Date of Award
2022-04-29Publisher
Te Herenga Waka—Victoria University of WellingtonRights License
CC BY-NC-SA 4.0Degree Discipline
MathematicsDegree Grantor
Te Herenga Waka—Victoria University of WellingtonDegree Level
MastersDegree Name
Master of ScienceANZSRC Type Of Activity code
1 Pure basic researchVictoria University of Wellington Item Type
Awarded Research Masters ThesisLanguage
en_NZVictoria University of Wellington School
School of Mathematics and StatisticsAdvisors
Clark, LisaUsage metrics
Keywords
Leavitt path algebras over arbitrary ringsIdealsLatticeSchool: School of Mathematics and Statistics010101 Algebra and Number Theory010107 Mathematical Logic, Set Theory, Lattices and Universal AlgebraDegree Discipline: MathematicsDegree Level: MastersDegree Name: Master of ScienceMathematical Logic, Set Theory, Lattices and Universal AlgebraAlgebra and Number Theory