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Ole Enge (2000)
Colloquium Mathematicae
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We show that a quasitilted algebra has a preprojective component. This is proved by giving an algorithmic criterion for the existence of preprojective components.
Gabriella D'Este (2006)
Commentationes Mathematicae Universitatis Carolinae
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We construct non faithful direct summands of tilting (resp. cotilting) modules large enough to inherit a functorial tilting (resp. cotilting) behaviour.
Clezio Braga, Flávio Coelho (2008)
Open Mathematics
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We discuss the existence of tilting modules which are direct limits of finitely generated tilting modules over tilted algebras.
Rüdiger Göbel, Daniel Simson (1998)
Colloquium Mathematicae
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Gabriella D'Este, Dieter Happel (1990)
Rendiconti del Seminario Matematico della Università di Padova
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Bertha Tomé (1995)
Fundamenta Mathematicae
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Let Λ be a finite-dimensional, basic and connected algebra over an algebraically closed field, and mod Λ be the category of finitely generated right Λ-modules. We say that Λ has acceptable projectives if the indecomposable projective Λ-modules lie either in a preprojective component without injective modules or in a standard coil, and the standard coils containing projectives are ordered. We prove that for such an algebra Λ the following conditions are equivalent: (a) Λ is tame, (b)...
Zygmunt Pogorzały, Karolina Szmyt (2007)
Open Mathematics
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We consider a class of algebras whose Auslander-Reiten quivers have starting components that are not generalized standard. For these components we introduce a generalization of a slice and show that only in finitely many cases (up to isomorphism) a slice module is a tilting module.