Algebren, Darstellungsköcher, Ueberlagerungen und zurück.
Algèbres auto-injectives de représentation finie
Algèbres de Bass et extensions de Ore itérées.
We show that some iterated Ore extensions have the same behaviour with respect to injective resolutions as Gorenstein commutative rings.
Almost smooth algebras
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...
Anneaux biréguliers auto-injectifs à droite
Anneaux réguliers auto-injectifs à droite
Anneaux semi-artiniens non commutatifs
Behavior of countably generated pure-projective modules.
We first prove that every countably presented module is a pure epimorphic image of a countably generated pure-projective module, and by using this we prove that if every countably generated pure-projective module is pure-injective then every module is pure-injective, while if in any countably generated pure-projective module every countably generated pure-projective pure submodule is a direct summand then every module is pure-projective.
Bounds for the homological dimensions of pullbacks.
Calabi-Yau stable module categories of finite type
We describe the stable module categories of the self-injective finite-dimensional algebras of finite representation type over an algebraically closed field which are Calabi-Yau (in the sense of Kontsevich).
Cartan matrices of selfinjective algebras of tubular type
The Cartan matrix of a finite dimensional algebra A is an important combinatorial invariant reflecting frequently structural properties of the algebra and its module category. For example, one of the important features of the modular representation theory of finite groups is the nonsingularity of Cartan matrices of the associated group algebras (Brauer’s theorem). Recently, the class of all tame selfinjective algebras having simply connected Galois coverings and the stable Auslander-Reiten quiver...
Character modules, submodules of a free module, and quasi-Frobenius rings.
Characterizing rings by their modules
Classes of Modules.
Coherence relative to a weak torsion class
Let be a ring. A subclass of left -modules is called a weak torsion class if it is closed under homomorphic images and extensions. Let be a weak torsion class of left -modules and a positive integer. Then a left -module is called -finitely generated if there exists a finitely generated submodule such that ; a left -module is called -presented if there exists an exact sequence of left -modules such that are finitely generated free and is -finitely generated; a left -module...
Cohomologie locale de certains anneaux Auslander-Gorenstein.
We give axiomatic conditions in order to calculate the local cohomology of some idempotent kernel functors. These results lie in some new dimension introduced by T. Levasseur for Auslander-Gorenstein rings. Under some hypothesis, we generalize previous results.
Completions of Regular Rings.
Copure injective resolutions, flat resolvents and dimensions
In this paper, we show the existence of copure injective preenvelopes over noetherian rings and copure flat preenvelopes over commutative artinian rings. We use this to characterize -Gorenstein rings. As a consequence, if the full subcategory of strongly copure injective (respectively flat) modules over a left and right noetherian ring has cokernels (respectively kernels), then is -Gorenstein.
Corrigendum to the paper " Quotient rings and one-sided primes".