On the annihilators of generalized local cohomology modules

Document Type : Research Paper

Author

Department of Mathematics, Payame Noor University, Tehran, Iran

Abstract

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     $Ann_R(H_{\frak{m}}^{d+n}(M,N))\subseteq Ann_R Ext_R^d(M,N/T)$.

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References

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Journal of Mahani Mathematical Research
Volume 15, Issue 1 - Serial Number 33
January 2026
Pages 125-130

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History

  • Receive Date: 08 March 2025
  • Revise Date: 15 June 2025
  • Accept Date: 21 July 2025

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