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Demonstrates the properties of cousin functors in modules over rings, suggesting implications for algebraic structures.
Let R be a commutative Noetherian ring with non-zero identity and F a filtration of Spec(R). We show that the Cousin functor with respect to F, CR(F,-):CF(R)(R), where CF(R) is the category of R-modules which are admitted by F and Comp(R) is the category of complexes of R-modules, commutes with the formation of direct limits and is right exact. We observe that an R-module X is balanced big Cohen-Macaulay if (R,m) is a local ring, mX≠ X, and every finitely generated submodule of X is a big Cohen-Macaulay R-module with respect to some system of parameters for R.
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Vahidi et al. (2023) studied this question.
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