%0 Journal Article %T TWO PROPERTIES OF COUSIN FUNCTORS %J Journal of Algebraic Systems %I Shahrood University of Technology %Z 2345-5128 %A Vahidi, Alireza %A Hassani, Faisal %A Senshenas, Maryam %D 2023 %\ 09/01/2023 %V 11 %N 1 %P 27-36 %! TWO PROPERTIES OF COUSIN FUNCTORS %K ‎Cousin complexes‎ %K ‎Cousin functors‎ %K ‎direct limits‎ %K ‎right exact functors %R 10.22044/jas.2022.11632.1592 %X ‌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 $R$‌. %U https://jas.shahroodut.ac.ir/article_2664_303abbdd182a064a3e42f9c51c9ce28a.pdf