Adjoints, torsion theory and purity.
Affine quivers and canonical bases
Algebra invariants for finite directed graphs with relations.
Algebraically Compact Rings and Modules.
Algebras and Quaternion Defect Groups. I.
Algebras and Quaternion Defect Groups. II.
Algebras of polynomial growth
Algebras over Zero-Dimensional Rings.
Algebras stably equivalent to trivial extensions of hereditary algebras of type
The study of stable equivalences of finite-dimensional algebras over an algebraically closed field seems to be far from satisfactory results. The importance of problems concerning stable equivalences grew up when derived categories appeared in representation theory of finite-dimensional algebras [8]. The Tachikawa-Wakamatsu result [17] also reveals the importance of these problems in the study of tilting equivalent algebras (compare with [1]). In fact, the result says that if A and B are tilting...
Algebras standardly stratified in all orders
The aim of this work is to characterize the algebras which are standardly stratified with respect to any order of the simple modules. We show that such algebras are exactly the algebras with all idempotent ideals projective. We also deduce as a corollary a characterization of hereditary algebras, originally due to Dlab and Ringel.
Algebras whose Euler form is non-negative
Algebras with Cycle-Finite Derived Categories.
Algebras with hypercritical Tits form
Algebren, Darstellungsköcher, Ueberlagerungen und zurück.
Algèbres auto-injectives de représentation finie
Algèbres de type de représentation fini
Almost split sequences and module categories: A complementary view to Auslander-Reiten Theory
We take a complementary view to the Auslander-Reiten trend of thought: Instead of specializing a module category to the level where the existence of an almost split sequence is inferred, we explore the structural consequences that result if we assume the existence of a single almost split sequence under the most general conditions. We characterize the structure of the bimodule with an underlying ring solely assuming that there exists an almost split sequence of left -modules . and are...
Almost split sequences for non-regular modules
Let A be an Artin algebra and let be an almost split sequence of A-modules with the indecomposable. Suppose that X has a projective predecessor and Z has an injective successor in the Auslander-Reiten quiver of A. Then r ≤ 4, and r = 4 implies that one of the is projective-injective. Moreover, if is a source map with the indecomposable and X on an oriented cycle in , then t ≤ 4 and at most three of the are not projective. The dual statement for a sink map holds. Finally, if an arrow...
Almost Split Sequences over p-adic Rings.
An Application of a Theorem of Ziegler.