Galois coverings of representation-infinite algebras.
Galois extensions as functors of comodules.
Idempotent completion of pretriangulated categories
A pretriangulated category is an additive category with left and right triangulations such that these two triangulations are compatible. In this paper, we first show that the idempotent completion of a left triangulated category admits a unique structure of left triangulated category and dually this is true for a right triangulated category. We then prove that the idempotent completion of a pretriangulated category has a natural structure of pretriangulated category. As an application, we show that...
Localization of cliques and model theory. (Localisation des cliques et théorie des modèles.)
Modules commuting (via Hom) with some colimits
For every module we have a natural monomorphism and we focus our attention on the case when is also an epimorphism. Some other colimits are also considered.
Motifs de dimension finie
On sait que les groupes de Chow d’une variété projective ne sont pas de type fini, et ne peuvent même être paramétrés par une variété algébrique, en général. Pourtant, S.-I. Kimura et P. O’Sullivan ont conjecturé (indépendamment l’un de l’autre) que les motifs de Chow, définis en termes de correspondances algébriques modulo l’équivalence rationnelle, sont de “dimension finie”au sens où, tout comme les super-fibrés vectoriels, ils sont somme d’un facteur dont une puissance extérieure est nulle et...
On algebras of strongly unbounded representation type.
On coalgebras and linearly topological rings
On countable von Neumann regular rings
On indecomposable representations of quivers with zero-relations
On subfunctors of the identity
On the category of commutative connected graded Hopf algebras over a perfect field
On the structure of locally finite pure semisimple Grothendieck categories
Products of small modules
Module is said to be small if it is not a union of strictly increasing infinite countable chain of submodules. We show that the class of all small modules over self-injective purely infinite ring is closed under direct products whenever there exists no strongly inaccessible cardinal.
Representation-directed algebras form an open scheme
We apply van den Dries's test to the class of algebras (over algebraically closed fields) which are not representation-directed and prove that this class is axiomatizable by a positive quantifier-free formula. It follows that the representation-directed algebras form an open ℤ-scheme.
Representation-finite algebras and multiplicative bases.
Representation-finite triangular algebras form an open scheme
Let V be a valuation ring in an algebraically closed field K with the residue field R. Assume that A is a V-order such that the R-algebra Ā obtained from A by reduction modulo the radical of V is triangular and representation-finite. Then the K-algebra KA ≅ A ⊗V is again triangular and representation-finite. It follows by the van den Dries’s test that triangular representation-finite algebras form an open scheme.
Rings in Post algebras.
Selfinjective algebras of polynomial growth.
Separable Moduln von Algebren über Ringen.