Graded artin algebras, coverings and factor rings
| dc.contributor.author | Weaver, Martha Ellen | en |
| dc.contributor.committeechair | Green, Edward | en |
| dc.contributor.committeemember | Herdman, Terry L. | en |
| dc.contributor.committeemember | Fletcher, Peter | en |
| dc.contributor.committeemember | Brown, E.A. | en |
| dc.contributor.committeemember | Arnold, Jesse T. | en |
| dc.contributor.department | Mathematics | en |
| dc.date.accessioned | 2018-03-26T18:50:30Z | en |
| dc.date.available | 2018-03-26T18:50:30Z | en |
| dc.date.issued | 1986 | en |
| dc.description.abstract | Let (Γ,ρ) be a directed graph with relations. Let F: Γ’ → Γ be a topological covering. It is proved in this thesis that there is a set of relations ρ̅ on Γ such that the category of K-respresentations of Γ’ whose images under the covering functor satisfy ρ is equivalent to the category of finite-dimensional, grades KΓ/<ρ̅>-modules. If Γ’ is the universal cover of Γ, then this category is called the category of unwindable KΓ/<ρ>-modules. For arrow unique graphs it is shown that the category of unwindable KΓ/<ρ>-modules does not depend on <ρ>. Also, it is shown that for arrow unique graphs the finite dimensional uniserial KΓ/<ρ>-modules are unwindable. Let Γ be an arrow unique graph with commutativity relations, ρ. In Section 2, the concept of unwindable modules is used to determine whether a certain factor ring of KΓ/<ρ> is of finite representation type. In a different vein, the relationship between almost split sequences over Artin algebras and the almost split sequences over factor rings of such algebras is studied. Let Λ be an Artin algebra and let Λ̅ be a factor ring of Λ. Two sets of necessary and sufficient conditions are obtained for determining when an almost split sequence of Λ̅-modules remains an almost split sequence when viewed as a sequence of Λ-modules. | en |
| dc.description.degree | Ph. D. | en |
| dc.format.extent | v, 100 leaves | en |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.uri | http://hdl.handle.net/10919/82612 | en |
| dc.language.iso | en_US | en |
| dc.publisher | Virginia Polytechnic Institute and State University | en |
| dc.relation.isformatof | OCLC# 15174833 | en |
| dc.rights | In Copyright | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject.lcc | LD5655.V856 1986.W439 | en |
| dc.subject.lcsh | Artin algebras | en |
| dc.subject.lcsh | Artin rings | en |
| dc.title | Graded artin algebras, coverings and factor rings | en |
| dc.type | Dissertation | en |
| dc.type.dcmitype | Text | en |
| thesis.degree.discipline | Mathematics | en |
| thesis.degree.grantor | Virginia Polytechnic Institute and State University | en |
| thesis.degree.level | doctoral | en |
| thesis.degree.name | Ph. D. | en |
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