Preradical

In mathematics, a preradical is a subfunctor of the identity functor in the category of left modules over a ring with identity. The class of all preradicals over R-mod is denoted by R-pr. There is a natural order in R-pr given by, for any two preradicals formula_1 and formula_2, formula_3, if for any left R-module M, formula_4. With this order R-pr becomes a big lattice.