Some precovers and preenvelopes in functor categories

Let n >= 1 be an integer. A functor F is an element of (mod-R, Ab) is called n-strongly FP -injective if F is isomorphic to some functor - circle times M in (mod-R, Ab) with M an FPn-injective left R-module. A functor G is an element of ((mod-R)(op), Ab) is said to be n-strongly flat if G is isomorphic to some functor (-,N) in ((mod-R)(op), Ab) with N an FPn-flat right R-module. Precovers and preenvelopes by n-strongly FP-injective and n-strongly flat functors are investigated over a general ring. As applications, special rings are characterized in terms of this two classes of functors.