منابع مشابه
On Auslander–Reiten components for quasitilted algebras
An artin algebra A over a commutative artin ring R is called quasitilted if gl.dimA ≤ 2 and for each indecomposable finitely generated A-module M we have pdM ≤ 1 or idM ≤ 1. In [11] several characterizations of quasitilted algebras were proven. We investigate the structure and homological properties of connected components in the Auslander–Reiten quiver ΓA of a quasitilted algebra A. Let A be a...
متن کاملOn Auslander-Reiten components of algebras without external short paths
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 description of self-injective artin algebras whose Auslander-Reiten quiver admits a regular acyclic component without external short paths.
متن کاملThe Auslander-Reiten Conjecture for Group Rings
This paper studies the vanishing of $Ext$ modules over group rings. Let $R$ be a commutative noetherian ring and $ga$ a group. We provide a criterion under which the vanishing of self extensions of a finitely generated $Rga$-module $M$ forces it to be projective. Using this result, it is shown that $Rga$ satisfies the Auslander-Reiten conjecture, whenever $R$ has finite global dimension and $ga...
متن کاملAlmost Regular Auslander-reiten Components and Quasitilted Algebras
The problem of giving a general description of the shapes of AuslanderReiten components of an artin algebra has been settled for semiregular components (see [4, 9, 14]). Recently, S. Li has considered this problem for components in which every possible path from an injective module to a projective module is sectional. The result says that such a component is embeddable in some ZZ∆ with ∆ a quiv...
متن کاملPreprojective Modules and Auslander-Reiten Components
In [2], Auslander and Smalø introduced and studied extensively preprojective modules and preinjective modules over an artin algebra. We now call a module hereditarily preprojective or hereditarily preinjective if its submodules are all preprojective or its quotient modules are all preinjective, respectively. In [4], Coelho studied Auslander-Reiten components containing only hereditarily preproj...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1995
ISSN: 0022-4049
DOI: 10.1016/0022-4049(94)00133-7