A method is presented making it possible to construct -groups with a strong theory of quasi-divisors of finite character and with some prescribed properties as subgroups of restricted Hahn groups , where are finitely atomic root systems. Some examples of these constructions are presented.
We investigate how one can detect the dualizing property for a chain complex over a commutative local Noetherian ring . Our focus is on homological properties of contracting endomorphisms of , e.g., the Frobenius endomorphism when contains a field of positive characteristic. For instance, in this case, when is -finite and is a semidualizing -complex, we prove that the following conditions are equivalent: (i) is a dualizing -complex; (ii) for some ; (iii) and is derived -reflexive...
Soit un groupe algébrique semi-simple simplement connexe défini sur un corps algébriquement clos de caractéristique positive. Nous donnons une nouvelle preuve de l’existence d’un scindage de Frobenius de la variété des drapeaux de ainsi que de la nature -équivariante de celui-ci. L’outil principal est un scindage de l’endomorphisme de Frobenius défini sur toute l’algèbre des distributions de qui permet de « détordre » la structure des -modules.
Every relatively convex-compact convex subset of a locally convex space is contained in a Banach disc. Moreover, an upper bound for the class of sets which are contained in a Banach disc is presented. If the topological dual of a locally convex space is the -closure of the union of countably many -relatively countably compacts sets, then every weakly (relatively) convex-compact set is weakly (relatively) compact.
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.
Nous introduisons pour les systèmes linéaires constants les reconstructeurs intégraux et les correcteurs proportionnels-intégraux généralisés, qui permettent d’éviter le terme dérivé du PID classique et, plus généralement, les observateurs asymptotiques usuels. Notre approche, de nature essentiellement algébrique, fait appel à la théorie des modules et au calcul opérationnel de Mikusiński. Plusieurs exemples sont examinés.
For constant linear systems we are introducing integral reconstructors and generalized proportional-integral controllers, which permit to bypass the derivative term in the classic PID controllers and more generally the usual asymptotic observers. Our approach, which is mainly of algebraic flavour, is based on the module-theoretic framework for linear systems and on operational calculus in Mikusiński's setting. Several examples are discussed.