On torsion theories and open classes of linear modular lattices

Given a ring R, a bijection exists between torsion theories and idempotent radicals. Further, the class of hereditary torsion theories contains the skeleton of the open classes. In this work, we extend the notions and main results in R-Mod about torsion classes, torsion-free classes, and open classes to the category L-M of linear lattices, whose objects are complete modular lattices and whose morphisms are linear morphisms.