فهرست نشریات علمی دسترسی آزاد ایران

‎Let $R$ be a commutative Noetherian ring with non-zero identity and $\mathcal{F}$ a filtration of $\operatorname{Spec}(R)$‎. ‎We show that the Cousin functor with respect to $\mathcal{F}$‎, ‎$C_R(\mathcal{F},-):\mathcal{C}_{\mathcal{F}}(R)\longrightarrow\operatorname{Comp}(R)$‎, ‎where $\mathcal{C}_{\mathcal{F}}(R)$ is the category of $R$-modules which are admitted by $\mathcal{F}$ and $\operatorname{Comp}(R)$ 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 $(R,\mathfrak{m})$ is a local ring‎, ‎$\mathfrak{m}X\neq X$‎, ‎and every finitely generated submodule of $X$ is a big Cohen-Macaulay $R$-module with respect to some system of parameters for $R$‎.