We prove that finitely generated n-SG-projective modules are infinitely presented.

Let Λ be a finite dimensional algebra over an algebraically closed field k and Λ has tame representation type. In this paper, the structure of Hom-spaces of all pairs of indecomposable Λ-modules having dimension smaller than or equal to a fixed natural number is described, and their dimensions are calculated in terms of a finite number of finitely generated Λ-modules and generic Λ-modules. In particular, such spaces are essentially controlled by those of the corresponding generic modules.

We construct non faithful direct summands of tilting (resp. cotilting) modules large enough to inherit a functorial tilting (resp. cotilting) behaviour.

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.

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.

This paper is motivated by the question whether there is a nice structure theory of finitely generated modules over the Iwasawa algebra, i.e. the completed group algebra, $\Lambda$ of a $p$-adic analytic group $G$. For $G$ without any $p$-torsion element we prove that $\Lambda$ is an Auslander regular ring. This result enables us to give a good definition of the notion of a pseudo-null $\Lambda$-module. This is classical when $G={\mathbb{Z}}_p^k$ for some integer $k\ge 1$, but was previously unknown in the non-commutative case. Then the category of $\Lambda$-modules...

The aim of this note is to give an affirmative answer to a problem raised in [9] by J. Nehring and A. Skowroński, concerning the number of nonstable ℙ₁(K)-families of quasi-tubes in the Auslander-Reiten quivers of the trivial extensions of tubular algebras over algebraically closed fields K.

We use modules of finite length to compare various generalizations of the classical tilting and cotilting modules introduced by Brenner and Butler [BrBu].

Given an object in a category, we study its orbit algebra with respect to an endofunctor. We show that if the object is periodic, then its orbit algebra modulo nilpotence is a polynomial ring in one variable. This specializes to a result on Ext-algebras of periodic modules over Gorenstein algebras. We also obtain a criterion for an algebra to be of wild representation type.