ANNIHILATORS OF TOP LOCAL COHOMOLOGY MODULES DEFINED BY A PAIR OF IDEALS
ANNIHILATORS OF TOP LOCAL COHOMOLOGY MODULES DEFINED BY A PAIR OF IDEALS
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一对理想定义的顶级局部上同调模的歼灭子
DOI：
10.24330/ieja.586962
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发表时间：
2019
影响因子：
0.6
通讯作者：
S. Payrovi
中科院分区：
文献类型：
--
作者：
S. Karimi;S. Payrovi
设$R$是一个交换noether环，$I, $ J$是$R$的两个固有理想；设$M$是一个非零有限生成的$R$-模，其中$c={\rm cd}(I，J，M)$。本文首先引入$T_R(I，J，M)$作为$M$的最大子模块，具有${\rm cd}(I，J,T_R(I，J，M))<c$的性质，并用$M$的零子模块的约简初等分解来描述它。结果表明,$ {\ rm安}_R (H_ {I, J} ^ d (M)) = {\ rm安}_R (M / {T_R (I, J, M)}) $和$ {\ rm安}_R (H_{我}^ d (M)) = {\ rm安}_R (H_ {I, J} ^ d (M)) $,每当R是一个局部环,美元M维d美元美元与美元H_ {I, J} ^ d (M) \ \ \ neq0 $和$ J ^ tM \ subseteq T_R(我)对一些正整数t美元美元。
Let $R$ be a commutative Noetherian ring, $I, J$ two proper ideals of $R$ and let $M$ be a non-zero finitely generated $R$-module with $c={\rm cd}(I,J,M)$. In this paper, we first introduce $T_R(I,J,M)$ as the largest submodule of $M$ with the property that ${\rm cd}(I,J,T_R(I,J,M))<c$ and we describe it in terms of the reduced primary decomposition of zero submodule of $M$. It is shown that ${\rm Ann}_R(H_{I,J}^d(M))={\rm Ann}_R(M/{T_R(I,J,M)})$ and ${\rm Ann}_R(H_{I}^d(M))={\rm Ann}_R(H_{I,J}^d(M))$, whenever $R$ is a local ring, $M$ has dimension $d$ with $H_{I,J}^d(M)\\\neq0$ and $J^tM\subseteq T_R(I,M)$ for some positive integer $t$.