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Auslander-Reiten components containing modules of finite complexity
Norwegian University of Science and Technology, Faculty of Information Technology, Mathematics and Electrical Engineering, Department of Mathematical Sciences.
2011 (English)MasteroppgaveStudent thesis
Abstract [en]
Let R be a connected selfinjective Artin algebra. We prove that any almost split sequence ending at an Omega-perfect R-module of finite complexity has at most four non-projective summands in a chosen decomposition of the middle term into indecomposable modules. Moreover, we show that a chosen decomposition into indecomposable modules of the middle term of an almost split sequence ending at an R-module of complexity 1 lying in a regular component of the Auslander-Reiten quiver has at most two summands. Furthermore, we prove that the regular component is of type ZA_{infinity} or ZA_{infinity}/. We use this to study modules with eventually constant and eventually periodic Betti numbers.
Place, publisher, year, edition, pages
Institutt for matematiske fag , 2011. , 132 p.
Keyword [no]
ntnudaim:5832, MMA matematikk, Algebra
URN: urn:nbn:no:ntnu:diva-12937Local ID: ntnudaim:5832OAI: diva2:427899
Available from: 2011-06-29 Created: 2011-06-29

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