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2 Colloquium Mathematicum

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On minimal non-tilted algebras

100%

Coelho F. , de la Peña J. , Trepode S.

nr 1

71-84

A minimal non-tilted triangular algebra such that any proper semiconvex subcategory is tilted is called a tilt-semicritical algebra. We study the tilt-semicritical algebras which are quasitilted or one-point extensions of tilted algebras of tame hereditary type. We establish inductive procedures to decide whether or not a given strongly simply connected algebra is tilted.

The composite of irreducible morphisms in regular components

100%

Chaio C. , Platzeck M. , Trepode S.

Colloquium Mathematicum

2011

tom 123

nr 1

27-47

We study when the composite of n irreducible morphisms between modules in a regular component of the Auslander-Reiten quiver is non-zero and lies in the n+1-th power of the radical ℜ of the module category. We prove that in this case such a composite belongs to $ℜ^{∞}$. We apply these results to characterize those string algebras having n irreducible morphisms between band modules such that their composite is a non-zero morphism in $ℜ^{n+1}$.