论文标题
最佳本地共同学和林奇的猜想的歼灭者
Annihilator of Top Local Cohomology and Lynch's Conjecture
论文作者
论文摘要
让$ r $为可交换的noetherian戒指，$ \ mathfrak a $ a $ r $和$ n $ a $ n $ a non-Zero有限生成的$ r $ -module，带有$ n \ neq \ neq \ mathfrak a n $。令$ d $（分别$ c $）为最小（分别是最大）的非负整数$ i $，使得本地同胞$ \ operatatorName {h}^i _ {\ mathfrak a}（n）$是非零。在本文中，我们为当地共同体学模块的歼灭者提供了尖锐的界限，$ \ operatatorName {h}^d _ {\ mathfrak a}（n）$，$ \ operatatorname {另外，我们构建了林奇猜想的反例。
Let $R$ be a commutative Noetherian ring, $\mathfrak a$ a proper ideal of $R$ and $N$ a non-zero finitely generated $R$-module with $N\neq \mathfrak a N$. Let $d$ (respectively $c$) be the smallest (respectively greatest) non-negative integer $i$ such that the local cohomology $\operatorname{H}^i_{\mathfrak a}(N)$ is non-zero. In this paper, we provide sharp bounds under inclusion for the annihilators of the local cohomology modules $\operatorname{H}^d_{\mathfrak a}(N)$, $\operatorname{H}^c_{\mathfrak a}(N)$ and these annihilators are computed in certain cases. Also, we construct a counterexample to Lynch's conjecture.
