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Some bounds for the annihilators of local cohomology and Ext modules
Czechoslovak Mathematical Journal, Tome 72 (2022) no. 1, pp. 265-284
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Let $\mathfrak a$ be an ideal of a commutative Noetherian ring $R$ and $t$ be a nonnegative integer. Let $M$ and $N$ be two finitely generated $R$-modules. In certain cases, we give some bounds under inclusion for the annihilators of ${\rm Ext}^t_R(M, N)$ and ${\rm H}^t_{\mathfrak a}(M)$ in terms of minimal primary decomposition of the zero submodule of $M$, which are independent of the choice of minimal primary decomposition. Then, by using those bounds, we compute the annihilators of local cohomology and Ext modules in certain cases.
Let $\mathfrak a$ be an ideal of a commutative Noetherian ring $R$ and $t$ be a nonnegative integer. Let $M$ and $N$ be two finitely generated $R$-modules. In certain cases, we give some bounds under inclusion for the annihilators of ${\rm Ext}^t_R(M, N)$ and ${\rm H}^t_{\mathfrak a}(M)$ in terms of minimal primary decomposition of the zero submodule of $M$, which are independent of the choice of minimal primary decomposition. Then, by using those bounds, we compute the annihilators of local cohomology and Ext modules in certain cases.
DOI : 10.21136/CMJ.2021.0456-20
Classification : 13D07, 13D45
Keywords: local cohomology module; Ext module; annihilator; primary decomposition 
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Fathi, Ali. Some bounds for the annihilators of local cohomology and Ext modules. Czechoslovak Mathematical Journal, Tome 72 (2022) no. 1, pp. 265-284. doi: 10.21136/CMJ.2021.0456-20

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