On the Properties of Formal Local Cohomology Modules

Document Type : Research Paper

Author

Department of Sciences, Marand Branch, Islamic Azad university, Marand, Iran

Abstract

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.

Keywords

References

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History

  • Receive Date: 04 March 2022
  • Revise Date: 30 July 2022
  • Accept Date: 31 July 2022

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