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Subjects
16-XX Associative rings and algebras
16Gxx Representation theory of rings and algebras
16G70 Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers

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Finding a cluster-tilting object for a representation finite cluster-tilted algebra

M. A. Bertani-Økland, S. Oppermann, A. Wrålsen (2010)

Colloquium Mathematicae

We provide a technique to find a cluster-tilting object having a given cluster-tilted algebra as endomorphism ring in the finite type case.

Full embeddings of almost split sequences over split-by-nilpotent extensions

Ibrahim Assem, Dan Zacharia (1999)

Colloquium Mathematicae

Let R be a split extension of an artin algebra A by a nilpotent bimodule $_{A} Q_{A}$ , and let M be an indecomposable non-projective A-module. We show that the almost split sequences ending with M in mod A and mod R coincide if and only if $H o m_{A} (Q, τ_{A} M)$ = 0 and $M \otimes_{A} Q = 0$ .

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