Quasitilted algebras have been introduced as a proper generalization of tilted algebras. In an earlier article we determined necessary conditions for one-point extensions of decomposable finite-dimensional hereditary algebras to be quasitilted and not tilted. In this article we study algebras satisfying these necessary conditions in order to investigate to what extent the conditions are sufficient.

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 continue the study of ditalgebras, an acronym for "differential tensor algebras", and of their categories of modules. We examine extension/restriction interactions between module categories over a ditalgebra and a proper subditalgebra. As an application, we prove a result on representations of finite-dimensional tame algebras Λ over an algebraically closed field, which gives information on the extension/restriction interaction between module categories of some special algebras Λ₀, called convex...

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.

We prove that for algebras obtained by tilts from the path algebras of equioriented Dynkin diagrams of type Aₙ, the rings of semi-invariants are polynomial.

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.

Given a semiperfect two-sided noetherian ring Λ, we study two subcategories ${}_k\left(\Lambda \right)=M\in mod\Lambda |Ex{t}_{\Lambda }^j(TrM,\Lambda )=0\left(1\le j\le k\right)$ and ${}_k\left(\Lambda \right)=N\in mod\Lambda |Ex{t}_{\Lambda }^j(N,\Lambda )=0\left(1\le j\le k\right)$ of the category mod Λ of finitely generated right Λ-modules, where Tr M is Auslander’s transpose of M. In particular, we give another convenient description of the categories ${}_k\left(\Lambda \right)$ and ${}_k\left(\Lambda \right)$, and we study category equivalences and stable equivalences between them. Several results proved in [J. Algebra 301 (2006), 748-780] are extended to the case when Λ is a two-sided noetherian semiperfect ring.

Let F: R → R/G be a Galois covering and $mo{d}_1(R/G)$ (resp. $mo{d}_2(R/G)$) 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 $\left(mod(R/G)\right)/\left[mo{d}_1(R/G)\right]$ and $mo{d}_2(R/G)$ is given in terms of representation categories of stabilizers of weakly-G-periodic modules for some class of coverings.