The structure of an almost artinian module.
The Structure of Certain Ideal Transforms.
The structure of indecomposable injective modules.
The tame degree and related invariants of non-unique factorizations
Local tameness and the finiteness of the catenary degree are two crucial finiteness conditions in the theory of non-unique factorizations in monoids and integral domains. In this note, we refine the notion of local tameness and relate the resulting invariants with the usual tame degree and the -invariant. Finally we present a simple monoid which fails to be locally tame and yet has nice factorization properties.
The tensor product of polynomials.
The theory of quasi-divisors on cartesian products
The theta ideal, dense submodules and the forcing linearity number for a multiplication module.
The torsion problem of H.-J. Reiffen and U. Vetter
The torsion theory and the Melkersson condition
We consider a generalization of the notion of torsion theory, which is associated with a Serre subcategory over a commutative Noetherian ring. In 2008 Aghapournahr and Melkersson investigated the question of when local cohomology modules belong to a Serre subcategory of the module category. In their study, the notion of Melkersson condition was defined as a suitable condition in local cohomology theory. One of our purposes in this paper is to show how naturally the concept of Melkersson condition...
The total graph of a module
The total torsion element graph of a module over a commutative ring.
The tropical Grassmannian.
The valuated ring of the arithmetical functions as a power series ring
The paper examines the ring of arithmetical functions, identifying it to the domain of formal power series over in a countable set of indeterminates. It is proven that is a complete ultrametric space and all its continuous endomorphisms are described. It is also proven that is a quasi-noetherian ring.
The Waring loci of ternary quartics.
The work of Jan-Erik Roos on the cohomology of commutative rings.
The Zariski category of graded commutative rings
The Zero-Dimensional Galois Cohomology of Witt Rings.
Théorème de Hilbert-Samuel «arithmétique»
On donne une nouvelle démonstration directe du théorème de Hilbert-Samuel arithmétique et on déduit un critère numérique pour l’existence de sections d’un fibré en droite sur une variété arithmétique de norme sup inférieure à un.
Théorème de Kaplansky effectif pour des valuations de rang 1 centrées sur des anneaux locaux réguliers et complets
On montre que tout anneau local régulier complet muni d’une valuation de rang peut être plongé, en tant qu’anneau valué, dans un anneau de séries de Puiseux généralisées.
Théorème des zéros effectif et élimination
Les paragraphes 1 et 2 rappellent les circonstances de l'exposé oral, tandis que le paragraphe 3 aborde un aspect particulier de la théorie de l'élimination : une notion de multiplicité d'un idéal en un point. Cette partie est le fruit de passionnantes discussions avec F. Amoroso.