Abstract
Let R be a commutative Noetherian ring, be an ideal of R, be a Serre subcategory of R-modules satisfying the condition , N be a finitely generated R-module and M be an arbitrary R-module with . We show that if M is an --cofinite R-module with , then is --cofinite for each . If with , then M is --cofinite if and only if Moreover, we prove that the subcategory and M is --cofinite of the category of R-modules is abelian. Furthermore, for a nonnegative integer n, we prove that for all if and only if is --cofinite for all and .
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