Adjoint Preenvelopes And Precovers Of Complexes

We give the definition of adjoint preenvelope and precover of complexes,study the existence and some properties of adjoint preenvelope and precover of complex-es,and discuss the relationship among adjoint preenvelope,adjoint precover,preen-velope and precover of complexes.As applications,we characterize some classical rings in terms of adjoint preenvelope and adjoint precover.