On lattices associated to rings with respect to a preradical

Abstract

We introduce some new lattices of classes of modules with respect to appropriate preradicals. We introduce some concepts associated with these lattices, such as the σ-semiartinian rings, the σ-retractable modules, the σ-V -rings, the σ-max rings. We continue to study σ-torsion theories, σ-open classes, σ-stable classes. We prove some theorems that extend some known results. Our results fall into well known situations when the preradical σ is chosen as the identity preradical.