Almost split sequences for non-regular modules

S. Liu

The search session has expired. Please query the service again.

Displaying similar documents to “Almost split sequences for non-regular modules”

On artin algebras with almost all indecomposable modules of projective or injective dimension at most one

Andrzej Skowroński (2003)

Open Mathematics

Similarity:

Let A be an artin algebra over a commutative artin ring R and ind A the category of indecomposable finitely generated right A-modules. Denote $ℒ_{A}$ to be the full subcategory of ind A formed by the modules X whose all predecessors in ind A have projective dimension at most one, and by $ℛ_{A}$ the full subcategory of ind A formed by the modules X whose all successors in ind A have injective dimension at most one. Recently, two classes of artin algebras A with $ℒ_{A} \cup ℛ_{A}$ co-finite in ind A, quasi-tilted...

Degenerations in the Module Varieties of Generalized Standard Auslander-Reiten Components

Grzegorz Zwara (1997)

Colloquium Mathematicae

Similarity:

Constructing the directing components of an algebra

J. de la Peña, M. Takane (1997)

Colloquium Mathematicae

Similarity:

A duality result for almost split sequences

Lidia Hügel, Helmut Valenta (1999)

Colloquium Mathematicae

Similarity:

Over an artinian hereditary ring R, we discuss how the existence of almost split sequences starting at the indecomposable non-injective preprojective right R-modules is related to the existence of almost split sequences ending at the indecomposable non-projective preinjective left R-modules. This answers a question raised by Simson in [27] in connection with pure semisimple rings.

Wild tilted algebras revisited

Otto Kerner (1997)

Colloquium Mathematicae

Similarity:

On the numbers of discrete indecomposable modules over tame algebras

Andrzej Skowroński, Grzegorz Zwara (1997)

Colloquium Mathematicae

Similarity:

Degenerations for modules over representation-finite selfinjective algebras

Grzegorz Zwara (1998)

Colloquium Mathematicae

Similarity:

On quasitilted algebras which are one-point extensions of hereditary algebras

Dieter Happel, Inger Slungård (1999)

Colloquium Mathematicae

Similarity:

Quasitilted algebras have been introduced as a proper generalization of tilted algebras. In an earlier article we determined necessary conditions for one-point extensions of decomposable finite-dimensional hereditary algebras to be quasitilted and not tilted. In this article we study algebras satisfying these necessary conditions in order to investigate to what extent the conditions are sufficient.

A characterization of representation-finite algebras

Andrzej Skowroński, M. Wenderlich (1991)

Fundamenta Mathematicae

Similarity:

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.

On the dynamics of $ϕ : x \to x^{p} + a$ in a local field

David Adam, Youssef Fares (2010)

Actes des rencontres du CIRM

Similarity:

Let $K$ be a local field, $a \in K$ and $ϕ : x \to x^{p} + a$ where $p$ denotes the characteristic of the residue field. We prove that the minimal subsets of the dynamical system $(K, ϕ)$ are cycles and describe the cycles of this system.