Symmetric Functions, Conjugacy Classes and the Flag Variety.
Systèmes dynamiques contraints : l'approche homologique
On décrit une approche homologique des systèmes dynamiques contraints. Cette approche, directement inspirée des travaux de D. McMullan et de M. Henneaux concernant le formalisme de Batalin, Fradkin et Vilkovisky, contient une interprétation des fantômes et de leurs conjugués. Dans le cadre des systèmes dans l’espace des phases, la construction se fait en deux étapes. La première étape consiste à construire une algèbre différentielle graduée dont la cohomologie en degré zéro est l’espace des observables...
The category of abelian Hopf algebras
The category of groupoid graded modules
We introduce the abelian category R-gr of groupoid graded modules and give an answer to the following general question: If U: R-gr → R-mod denotes the functor which associates to any graded left R-module M the underlying ungraded structure U(M), when does either of the following two implications hold: (I) M has property X ⇒ U(M) has property X; (II) U(M) has property X ⇒ M has property X? We treat the cases when X is one of the properties: direct summand, free, finitely generated, finitely presented,...
The cocycle equation in division rings.
The Cohomology Ring of a Monomial Algebra.
The Divisor Class Group of Ordinary and Symbolic Blow-ups.
The free -ring is a graded -ring.
The -graded identities of the Grassmann Algebra
Let be a finite abelian group with identity element and be an infinite dimensional -homogeneous vector space over a field of characteristic . Let be the Grassmann algebra generated by . It follows that is a -graded algebra. Let be odd, then we prove that in order to describe any ideal of -graded identities of it is sufficient to deal with -grading, where , and if . In the same spirit of the case odd, if is even it is sufficient to study only those -gradings such that...
The Radius of Convergence of Poincaré Series of Loop Spaces.
The smallest singularity of a Hilbert series.
Traces in strict Frobenius algebras and strict complete intersections.
Ultraproduits gradués. Applications.
Dans ce travail sont définis les ultraproduits d'anneaux et de modules gradués. L'ultraproduit gradué coïncide dans le case d'une famille Ri[X1, ..., Xn], i ∈ I, d'anneaux de polynômes avec le sousanneau d'éléments génerés dans l'ultraproduit usuel par les familles de polynômes de degré total borné.Nous démonstrons que l'ultraproduit d'une famille de modules gradués libres, qui verifie une condition naturelle de finitude et aussi un module gradué libre (Théorème 2.2). Après un étude de l'arithmétique...
Weak Baer modules over graded rings
In [2], Fuchs and Viljoen introduced and classified the -modules for a valuation ring R: an R-module M is a -module if for each divisible module X and each torsion module X with bounded order. The concept of a -module was extended to the setting of a torsion theory over an associative ring in [14]. In the present paper, we use categorical methods to investigate the -modules for a group graded ring. Our most complete result (Theorem 4.10) characterizes -modules for a strongly graded ring R...
Weak dimension of group-graded rings.
We study the weak dimension of a group-graded ring using methods developed in [B1], [Q] and [R]. We prove that if R is a G-graded ring with G locally finite and the order of every subgroup of G is invertible in R, then the graded weak dimension of R is equal to the ungraded one.
When are induction and coinduction functors isomorphic?
Алгебры, заданные двумя квадратичными соотношениями
Конечная базируемость тождеств ассоциативных алгебр
О 2-порожденных p-группах Голода
О некоммутативных инвариантах редуктивных групп.