Necessary and sufficient
conditions are obtained for the splitting of a hereditary cotorsion radical on the
category ℳR of right R-modules. It is shown that for injective cogenerator
rings and orders in semi-simple rings, all hereditary cotorsion radicals split.
Several other questions are also discussed. These include the relationship
between cotorsion radicals for ℳR and Rℳ, and the connection between
the properties of a projective module and those of the cotorsion radical it
induces.