On pure semisimplicity and representation-finite piecewise prime rings
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.
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.
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.
We give a complete description of all finite-dimensional selfinjective algebras over an algebraically closed field whose component quiver has no short cycles.
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.
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.
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.
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.
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.
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.
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 .
We show that a quasitilted algebra has a preprojective component. This is proved by giving an algorithmic criterion for the existence of preprojective components.
The Dynkin and the extended Dynkin graphs are characterized by representations over the real numbers.