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On the annihilators of generalized local cohomology modules | ||
| Journal of Mahani Mathematical Research | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 31 تیر 1404 اصل مقاله (451.34 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmr.2025.24948.1774 | ||
| نویسنده | ||
| Shahram Rezaei* | ||
| Department of Mathematics, Payame Noor University, Tehran, Iran | ||
| چکیده | ||
| Let ${\frak{a}}$ be an ideal of Noetherian ring $R$ and $M$, $N$ be two finitely generated $R$-modules. In this paper, we obtain some results about the annihilators of top generalized local cohomology modules. We define $T:=T_R(\frak{a},M, N)$ as the largest submodule of $N$ such that\\ $cd(\frak{a},M, T_R(\frak{a},M,N))<\operatorname{cd}(\frak{a},M,N)$. Let $(R,\frak{m})$ be a complete Gorenstein Noetherian local ring such that $pd(M)=d<\infty$, $dim\ N=dim\ R=n<\infty$ and $cd(\frak{a},M,N)=d+n$. We prove that if $Ass_R(Ext_R^d(M,N/T))\subseteq Ass_R R$, then $Ann_R(H_{\frak{m}}^{d+n}(M,N))\subseteq Ann_R Ext_R^d(M,N/T)$. | ||
| کلیدواژه‌ها | ||
| Annihilator؛ local cohomology؛ generalized local cohomology | ||
| مراجع | ||
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