Displaying similar documents to “On artin algebras with almost all indecomposable modules of projective or injective dimension at most one”

Substructures of algebras with weakly non-negative Tits form.

José Antonio de la Peña, Andrzej Skowronski (2007)

Extracta Mathematicae

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Let A = kQ/I be a finite dimensional basic algebra over an algebraically closed field k presented by its quiver Q with relations I. A fundamental problem in the representation theory of algebras is to decide whether or not A is of tame or wild type. In this paper we consider triangular algebras A whose quiver Q has no oriented paths. We say that A is essentially sincere if there is an indecomposable (finite dimensional) A-module whose support contains all extreme vertices of Q. We prove...

A characterization of representation-finite algebras

Andrzej Skowroński, M. Wenderlich (1991)

Fundamenta Mathematicae

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Let A be a finite-dimensional, basic, connected algebra over an algebraically closed field. Denote by Γ(A) the Auslander-Reiten quiver of A. We show that A is representation-finite if and only if Γ(A) has at most finitely many vertices lying on oriented cycles and finitely many orbits with respect to the action of the Auslander-Reiten translation.

Componentwise injective models of functors to DGAs

Marek Golasiński (1997)

Colloquium Mathematicae

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The aim of this paper is to present a starting point for proving existence of injective minimal models (cf. [8]) for some systems of complete differential graded algebras.