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On the Properties of Formal Local Cohomology Modules | ||
| Journal of Mahani Mathematical Research | ||
| دوره 12، شماره 2 - شماره پیاپی 25، مرداد 2023، صفحه 1-6 اصل مقاله (431.67 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmr.2022.19129.1212 | ||
| نویسنده | ||
| Behruz Sadeqi* | ||
| Department of Sciences, Marand Branch, Islamic Azad university, Marand, Iran | ||
| چکیده | ||
| Let $(R,m)$ be a commutative Noetherian local ring, $a$ an ideal of $R$. Let $t\in\Bbb N_0$ be an integer and $M$ a finitely generated $R$-module such that the $R$-module $\mathfrak{F}^i_{\mathfrak{a}}(M)$ is $\mathfrak{a}$-cominimax for all $i<t$. We prove that For all minimax submodules $N$ of $\mathfrak{F}^i_{\mathfrak{a}}(M)$, the $R$-modules \[ Hom_R(R/\mathfrak{a},\mathfrak{F}^t_{\mathfrak{a}}(M)/N)\hspace{5mm} and \hspace{5mm}Ext^1_R(R/\mathfrak{a},\mathfrak{F}^t_{\mathfrak{a}}(M)/N) \] are minimax. In particular, the set $Ass_R(\mathfrak{F}^t_{\mathfrak{a}}(M)/N)$ is finite. | ||
| کلیدواژه‌ها | ||
| formal local cohomology modules؛ local cohomology؛ cominimax modules | ||
| مراجع | ||
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