Coherent Rings and Homologically Finite Subcategories.
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.
Cohomology of algebras of dihedral type. I.
Colimits of representable algebra-valued functors.
Commutative rings whose certain modules decompose into direct sums of cyclic submodules
We provide some characterizations of rings for which every (finitely generated) module belonging to a class of -modules is a direct sum of cyclic submodules. We focus on the cases, where the class is one of the following classes of modules: semiartinian modules, semi-V-modules, V-modules, coperfect modules and locally supplemented modules.
...-Compactness of Reuced Products and Filter Quotients.
Comparison of abelian categories recollements.
Compatible ideals and radicals of Ore extensions.
Completely O-simple multiplicative ideals of rings.
Completely Prime Radical and Primary Ideal Representations in Non-Commutative Rings.
Completions of Regular Rings.
Composition-diamond lemma for modules
We investigate the relationship between the Gröbner-Shirshov bases in free associative algebras, free left modules and “double-free” left modules (that is, free modules over a free algebra). We first give Chibrikov’s Composition-Diamond lemma for modules and then we show that Kang-Lee’s Composition-Diamond lemma follows from it. We give the Gröbner-Shirshov bases for the following modules: the highest weight module over a Lie algebra , the Verma module over a Kac-Moody algebra, the Verma module...
Comultiplication modules over a pullback of Dedekind domains
First, we give complete description of the comultiplication modules over a Dedekind domain. Second, if is the pullback of two local Dedekind domains, then we classify all indecomposable comultiplication -modules and establish a connection between the comultiplication modules and the pure-injective modules over such domains.
Consistent algebras and special tilting sequences.
Constructions and homological properties of simple von Neumann regular rings
Control subgroups and birational extensions of graded 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".
Costable rings
Countably thick modules
The purpose of this paper is to further the study of countably thick modules via weak injectivity. Among others, for some classes of modules in we study when direct sums of modules from satisfies a property in . In particular, we get characterization of locally countably thick modules, a generalization of locally q.f.d. modules.