TWO PROPERTIES OF COUSIN FUNCTORS

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, −) : C (R) −→ Comp(R), where C (R) is the category of R-modules Fwhich are admitted by F andF 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