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Cofiniteness with respect to a Serre subcategory |
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| Authors: | A Hajikarimi | |
| Institution: | 1. Mobarakeh Branch, Islamic Azad University, Isfahan, Iran |
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| Abstract: | Let Φ be a system of ideals in a commutative Noetherian ring R, and let  $$ H_\Phi ^i ( \cdot , \cdot ) = \mathop {\lim }\limits_{\overrightarrow {\mathfrak{b} \in \Phi } } Ext_R^i (R/\mathfrak{b}| \otimes R \cdot , \cdot ). $$ . Suppose that a is an ideal of R, and M and N are two R-modules such that M is finitely generated and N ∈  $ D_\Phi ( \cdot ) = \mathop {\lim }\limits_{\overrightarrow {\mathfrak{b} \in \Phi } } Hom_R (\mathfrak{b}, \cdot ) $ is exact, then, for any $ \mathfrak{b} \in \Phi ,Ext_R^j (R/\mathfrak{b},H_\Phi ^i (M,N)) $ ∈  $ H_\mathfrak{a}^i (M,N) $ ∈  $ Hom_R (R/\mathfrak{a},H_\mathfrak{a}^t (M,N)) $ ∈   $ H_\mathfrak{a}^i (L) $ ∈  $ Ext_R^j (R/\mathfrak{a},H_\mathfrak{a}^t (M,L)) $ ∈  $ Ext_R^j (R/\mathfrak{a},Hom_R (M,H_\mathfrak{a}^t (L))) $ ∈  | |
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