TWO PROPERTIES OF COUSIN FUNCTORS | ||
| Journal of Algebraic Systems | ||
| دوره 11، شماره 1، آذر 2023، صفحه 27-36 اصل مقاله (148.75 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2022.11632.1592 | ||
| نویسندگان | ||
| Alireza Vahidi* ؛ Faisal Hassani؛ Maryam Senshenas | ||
| Department of Mathematics, Payame Noor University, Tehran, Iran. | ||
| چکیده | ||
| 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 $R$. | ||
| کلیدواژهها | ||
| Cousin complexes؛ Cousin functors؛ direct limits؛ right exact functors | ||
| مراجع | ||
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10. R. Y. Sharp, The Cousin complex for a module over a commutative Noetherian ring, Math. Z., 112 (1969), 340–356. | ||
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آمار تعداد مشاهده مقاله: 180 تعداد دریافت فایل اصل مقاله: 239 |
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