Centrally splitting radicals
Let be an associative ring and be a left -module. We introduce the concept of the incidence module of a locally finite partially ordered set over . We study the properties of and give the necessary and sufficient conditions for the incidence module to be an IN-module, -module, nil injective module and nonsingular module, respectively. Furthermore, we show that the class of -modules is closed under direct product and upper triangular matrix modules.
We characterize semiperfect modules, semiperfect rings, and perfect rings using locally projective covers and generalized locally projective covers, where locally projective modules were introduced by Zimmermann-Huisgen and generalized locally projective covers are adapted from Azumaya’s generalized projective covers.
Let be the -dimensional Radford Hopf algebra over an algebraically closed field of characteristic zero. We give the classification of all ideals of -dimensional Radford Hopf algebra by generators.
Si considerano le estensioni chiuse di un -modulo mediante un -modulo nel caso in cui sia un anello semi-artiniano, cioè un anello con la proprietà che per ogni quoziente sia soc . Tali estensioni sono caratterizzate dal fatto che deve essere un sottomodulo semi-puro di .
Soit la première algèbre de Weyl sur . La codimension B-W d’un idéal à droite non nul de a été introduite par Yuri Berest et George Wilson. Nous montrons d’une part que cette codimension est invariante par la relation de Stafford : si , le corps de fractions de , et si , le groupe des -automorphismes de , sont tels que soit un idéal à droite de , alors . Nous relions d’autre part la codimension d’un idéal à la codimension de Gail Letzter-Makar Limanov, de , l’anneau des endomorphismes...