On the inverse operations in the class of preradicals of a module category

Abstract

In the class PR of preradicals of the category of left R-modules RMod a new operation is defined and studied, namely the left quotient with respect to join. Some properties of this operation are shown, its compatibility with the lattice operations of PR (meet and join of preradicals), as well as the relations with some constructions in the "big" lattice PR . Also some particular cases are examined.