Inyectividad pura y dimensión débil.
Laura algebras and quasi-directed components
Using a notion of distance between indecomposable modules we deduce new characterizations of laura algebras and quasi-directed Auslander-Reiten components. Afterwards, we investigate the infinite radical of Artin algebras and show that there exist infinitely many non-directing modules between two indecomposable modules X and Y if . We draw as inference that a convex component is quasi-directed if and only if it is almost directed.
Left global dimensions and inverse polynomial modules.
Left sections and the left part of an artin algebra
We define a notion of left section in an Auslander-Reiten component, by weakening one of the axioms for sections. We derive a generalisation of the Liu-Skowroński criterion for tilted algebras, then apply our results to describe the Auslander-Reiten components lying in the left part of an artin algebra.
Maps of cotriples and a change of rings theorem
Maximal Orders of global dimension and Krull dimension two.
Modules of finite projective dimension and cocovers.
Modules over regular algebras of dimension 3.
Modules over the 4-dimensional Sklyanin algebra
-flat and -FP-injective modules
In this paper, we study the existence of the -flat preenvelope and the -FP-injective cover. We also characterize -coherent rings in terms of the -FP-injective and -flat modules.
On artin algebras with almost all indecomposable modules of projective or injective dimension at most one
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 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 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 co-finite in ind A, quasi-tilted algebras and...
On Auslander–Reiten components for quasitilted algebras
An artin algebra A over a commutative artin ring R is called quasitilted if gl.dim A ≤ 2 and for each indecomposable finitely generated A-module M we have pd M ≤ 1 or id M ≤ 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 of a quasitilted algebra A.
On Filtered Modules and their Associated Graded Modules.
On Gorenstein Rings.
On minimal non-tilted algebras
A minimal non-tilted triangular algebra such that any proper semiconvex subcategory is tilted is called a tilt-semicritical algebra. We study the tilt-semicritical algebras which are quasitilted or one-point extensions of tilted algebras of tame hereditary type. We establish inductive procedures to decide whether or not a given strongly simply connected algebra is tilted.
On presented dimensions of modules and rings.
On projective resolutions of flat modules
On pure global dimension of locally finitely presented Grothendieck categories
On the Auslander-Reiten valued quiver of right peak rings
On the derived category of a finite-dimensional algebra.