Cotorsion pair extensions

Assume that S is an almost excellent extension of R. Using functors HomR(S,−) and —⊗RS, we establish some connections between classes of modules [graphic not available: see fulltext] and [graphic not available: see fulltext], cotorsion pairs [graphic not available: see fulltext] and [graphic not available: see fulltext]. If [graphic not available: see fulltext] is a T-extension or (and) H-extension of [graphic not available: see fulltext], we show that [graphic not available: see fulltext] is a (resp., monomorphic, epimorphic, special) preenveloping class if and only if so is [graphic not available: see fulltext]. If [graphic not available: see fulltext] is a TH-extension of [graphic not available: see fulltext], we obtain that [graphic not available: see fulltext] is complete (resp., of finite type, of cofinite type, hereditary, perfect, n-tilting) if and only if so is [graphic not available: see fulltext].