@article {
author = {Vahidi, Alireza and Hassani, Faisal and Senshenas, Maryam},
title = {TWO PROPERTIES OF COUSIN FUNCTORS},
journal = {Journal of Algebraic Systems},
volume = {11},
number = {1},
pages = {27-36},
year = {2023},
publisher = {Shahrood University of Technology},
issn = {2345-5128},
eissn = {2345-511X},
doi = {10.22044/jas.2022.11632.1592},
abstract = {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 $R$.},
keywords = {Cousin complexes,Cousin functors,direct limits,right exact functors},
url = {https://jas.shahroodut.ac.ir/article_2664.html},
eprint = {https://jas.shahroodut.ac.ir/article_2664_303abbdd182a064a3e42f9c51c9ce28a.pdf}
}