Acta Mathematica Sinica. 2009, 25(9): 0-0.
Assume that S is an almost excellent extension of R.
Using functors Hom_R(S,-) and -\otimes_RS, we establish some
connections between classes of modules C_R and C_S,
cotorsion pairs (A_R, B_R) and (A_S,B_S). If C_S is a T-extension or (and) H-extension of C_R, we show that
C_S is a (monomorphic, epimorphic, special) preenveloping class
if and only if so is C_R. If (A_S,B_S) is a
TH-extension of (A_R, B_R), we obtain that (A_S,B_S) is complete (of finite type, of cofinite type, hereditary,
perfect, n-tilting) if and only if so is (A_R,B_R).