Consider a finite acyclic quiver Q and a quasi-Frobenius ring R. We endow the category of quiver representations over R with a model structure, whose homotopy category is equivalent to the stable category of Gorenstein-projective modules over the path algebra RQ. As an application, we then characterize Gorenstein-projective RQ-modules in terms of the corresponding quiver R-representations; this generalizes a result obtained by Luo-Zhang to the case of not necessarily finitely generated RQ-modules, and partially recover results due to Enochs-Estrada-García Rozas, and to Eshraghi-Hafezi-Salarian. Our approach to the problem is completely different since the proofs mainly rely on model category theory
Let R be a complete local Gorenstein ring of dimension one, with maximal ideal m. We show ...
Let $\varphi\colon R\rightarrow A$ be a ring homomorphism, where $R$ is a commutative noetherian rin...
We study three triangulated categories associated to a Gorenstein ring, that is, a right- and left-n...
Consider a finite acyclic quiver Q and a quasi-Frobenius ring R. We endow the category of quiver rep...
We consider a finite acyclic quiver $\mathcalQ$ and a quasi-Frobenius ring $R$. We then characteris...
We introduce a notion of Gorenstein quiver associated witha Gorenstein matrix. We study properties o...
AbstractWe study Artin algebras Λ and commutative Noetherian complete local rings R in connection wi...
In earlier work, the author classified rigid representations of a quiver by finitely generated free ...
In earlier work, the author classified rigid representations of a quiver by finitely generated free ...
We prove that algebras are left weakly Gorenstein in case the subcategory $^{\perp}A \cap \Omega^n(A...
Owing to the difference in $K$-theory, an example by Dugger and Shipley implies that the equivalence...
We give a result of Auslander-Ringel-Tachikawa type for Gorenstein-projective modules over a complet...
AbstractWe study Artin algebras Λ and commutative Noetherian complete local rings R in connection wi...
Abstract. It is shown that a morphism of quivers having a certain path lifting property has a decomp...
AbstractLet R be a ring and Q be a quiver. We study the homotopy categories K(PrjQ) and K(InjQ) cons...
Let R be a complete local Gorenstein ring of dimension one, with maximal ideal m. We show ...
Let $\varphi\colon R\rightarrow A$ be a ring homomorphism, where $R$ is a commutative noetherian rin...
We study three triangulated categories associated to a Gorenstein ring, that is, a right- and left-n...
Consider a finite acyclic quiver Q and a quasi-Frobenius ring R. We endow the category of quiver rep...
We consider a finite acyclic quiver $\mathcalQ$ and a quasi-Frobenius ring $R$. We then characteris...
We introduce a notion of Gorenstein quiver associated witha Gorenstein matrix. We study properties o...
AbstractWe study Artin algebras Λ and commutative Noetherian complete local rings R in connection wi...
In earlier work, the author classified rigid representations of a quiver by finitely generated free ...
In earlier work, the author classified rigid representations of a quiver by finitely generated free ...
We prove that algebras are left weakly Gorenstein in case the subcategory $^{\perp}A \cap \Omega^n(A...
Owing to the difference in $K$-theory, an example by Dugger and Shipley implies that the equivalence...
We give a result of Auslander-Ringel-Tachikawa type for Gorenstein-projective modules over a complet...
AbstractWe study Artin algebras Λ and commutative Noetherian complete local rings R in connection wi...
Abstract. It is shown that a morphism of quivers having a certain path lifting property has a decomp...
AbstractLet R be a ring and Q be a quiver. We study the homotopy categories K(PrjQ) and K(InjQ) cons...
Let R be a complete local Gorenstein ring of dimension one, with maximal ideal m. We show ...
Let $\varphi\colon R\rightarrow A$ be a ring homomorphism, where $R$ is a commutative noetherian rin...
We study three triangulated categories associated to a Gorenstein ring, that is, a right- and left-n...