16 citations · 59 across the 8 of their papers we have counts for
9 papers
Cycle-finite modules over artin algebras
Piotr Malicki, Andrzej Skowroński
We describe the representation theory of finitely generated indecomposable modules over artin algebras which do not lie on cycles of indecomposable modules involving homomorphisms…
The structure and homological properties of generalized standard Auslander-Reiten components
Piotr Malicki, Andrzej Skowroński
We describe the structure and homological properties of arbitrary generalized standard Auslander-Reiten components of artin algebras. In particular, we prove that for all but finit…
Finite cycles of indecomposable modules
Piotr Malicki, José Antonio de la Peña, Andrzej Skowroński
We solve a long standing open problem concerning the structure of finite cycles in the category mod A of finitely generated modules over an arbitrary artin algebra A, that is, the…
On the number of terms in the middle of almost split sequences over cycle-finite artin algebras
Piotr Malicki, José A. de la Peña, Andrzej Skowroński
We prove that the number of terms in the middle of an almost split sequence in the module category of a cycle-finite artin algebra is bounded by 5.
Cycle-finite module categories
Piotr Malicki, José A. de la Peña, Andrzej Skowroński
We describe the structure of module categories of finite dimensional algebras over an algebraically closed field for which the cycles of nonzero nonisomorphisms between indecomposa…
Classification of modules not lying on short chains
Alicja Jaworska, Piotr Malicki, Andrzej Skowroński
We give a complete description of finitely generated modules over artin algebras which are not the middle of a short chain of modules, using injective and tilting modules over here…
Tilted algebras and short chains of modules
Alicja Jaworska, Piotr Malicki, Andrzej Skowroński
We provide an affirmative answer for the question raised almost twenty years ago concerning the characterization of tilted artin algebras by the existence of a sincere finitely gen…
On Auslander-Reiten components of algebras without external short paths
Alicja Jaworska, Piotr Malicki, Andrzej Skowroński
We describe the structure of semi-regular Auslander-Reiten components of artin algebras without external short paths in the module category. As an application we give a complete de…
Auslander-Reiten Components determined by their Composition Factors
Alicja Jaworska, Piotr Malicki, Andrzej Skowroński
We provide sufficient conditions for a component of the Auslander-Reiten quiver of an artin algebra to be determined by the composition factors of its indecomposable modules.