On F -Almost Split Sequences
نویسندگان
چکیده
Let Λ be an Artinian algebra and F an additive subbifunctor of ExtΛ(−,−) having enough projectives and injectives. We prove that the dualizing subvarieties of mod Λ closed under F -extensions have F -almost split sequences. Let T be an F -cotilting module in mod Λ and S a cotilting module over Γ = End(T ). Then Hom(−, T ) induces a duality between F -almost split sequences in ⊥F T and almost split sequences in ⊥S, where addΓS = HomΛ(P(F ), T ). Let Λ be an F -Gorenstein algebra, T a strong F -cotilting module and 0 → A → B → C → 0 an F -almost split sequence in ⊥F T . If the injective dimension of S as a Γ-module is equal to d, then C ∼= (Ω−d CMΩDTrA), where (−)∗ = Hom(−, T ). In addition, if the F -injective dimension of A is equal to d, then A ∼= Ω−d CMF DΩ−d FopTrC ∼= Ω−d CMF ΩFDTrC.
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