On restrictions of generic modules of tame algebras
Given a convex algebra ∧0 in the tame finite-dimensional basic algebra ∧, over an algebraically closed field, we describe a special type of restriction of the generic ∧-modules.
On self-injective algebras of finite representation type
We describe the structure of finite-dimensional self-injective algebras of finite representation type over a field whose stable Auslander-Reiten quiver has a sectional module not lying on a short chain.
On selfinjective algebras of tilted type
We provide a characterization of all finite-dimensional selfinjective algebras over a field K which are socle equivalent to a prominent class of selfinjective algebras of tilted type.
On selfinjective algebras without short cycles in the component quiver
We give a complete description of all finite-dimensional selfinjective algebras over an algebraically closed field whose component quiver has no short cycles.
On selfinjective artin algebras having nonperiodic generalized standard Auslander-Reiten components
We describe the structure of all selfinjective artin algebras having at least three nonperiodic generalized standard Auslander-Reiten components. In particular, all selfinjective artin algebras having a generalized standard Auslander-Reiten component of Euclidean type are described.
On split-by-nilpotent extensions
Let A and R be two artin algebras such that R is a split extension of A by a nilpotent ideal. We prove that if R is quasi-tilted, or tame and tilted, then so is A. Moreover, generalizations of these properties, such as laura and shod, are also inherited. We also study the relationship between the tilting R-modules and the tilting A-modules.
On the Auslander-Reiten valued quiver of right peak rings
On the category of modules of second kind for Galois coverings
Let F: R → R/G be a Galois covering and (resp. ) be a full subcategory of the module category mod (R/G), consisting of all R/G-modules of first (resp. second) kind with respect to F. The structure of the categories and is given in terms of representation categories of stabilizers of weakly-G-periodic modules for some class of coverings.
On the existence of almost split sequences in subcategories
On the Freyd categories of an additive category.
On the lattice of cotilting modules.
On the number of terms in the middle of almost split sequences over cycle-finite artin algebras
We prove that the number of terms in the middle of an almost split sequence in the module category of a cycle-finite artin algebra is bounded by 5.
On the Represantation Theory of Artinian Rings and Artins Problems on Division Ring Extensions
On wings of the Auslander-Reiten quivers of selfinjective algebras
We give necessary and sufficient conditions for a wing of an Auslander-Reiten quiver of a selfinjective algebra to be the wing of the radical of an indecomposable projective module. Moreover, a characterization of indecomposable Nakayama algebras of Loewy length ≥ 3 is obtained.
Orbit algebras that are invariant under stable equivalences of Morita type
In this note we show that there are a lot of orbit algebras that are invariant under stable equivalences of Morita type between self-injective algebras. There are also indicated some links between Auslander-Reiten periodicity of bimodules and noetherianity of their orbit algebras.
Piecewise hereditary algebras under field extensions
Let be a finite-dimensional -algebra and be a finite separable field extension. We prove that is derived equivalent to a hereditary algebra if and only if so is .
Polynomial functors over finite fields
Quasitilted algebras have preprojective components
We show that a quasitilted algebra has a preprojective component. This is proved by giving an algorithmic criterion for the existence of preprojective components.
Real representations of quivers
The Dynkin and the extended Dynkin graphs are characterized by representations over the real numbers.
Relative Auslander-Reiten sequences for quasi-hereditary algebras
Let A be a finite-dimensional algebra which is quasi-hereditary with respect to the poset (Λ, ≤), with standard modules Δ(λ) for λ ∈ Λ. Let ℱ(Δ) be the category of A-modules which have filtrations where the quotients are standard modules. We determine some inductive results on the relative Auslander-Reiten quiver of ℱ(Δ).