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Volume 26, Issue 3
Some Results for Formal Local Cohomology Modules

Lizhong Chu

Commun. Math. Res., 26 (2010), pp. 230-238.

Published online: 2021-05

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  • Abstract

Let $(R, m)$ be a commutative Noetherian local ring, $I$ an ideal of $R$ and $M$ a finitely generated $R$-module. Let $\mathop{\rm lim}\limits_{\mathop{n} \limits ^{\longleftarrow}}H^i_m(M/I^nM)$ be the $i$th formal local cohomology module of $M$ with respect to $I$. In this paper, we discuss some properties of formal local cohomology modules $\mathop{\rm lim}\limits_{\mathop{n} \limits ^{\longleftarrow}}H^i_m(M/I^nM)$, which are analogous to the finiteness and Artinianness of local cohomology modules of a finitely generated module.

  • Keywords

local cohomology, formal local cohomology, coartinian module, minimax module, Artinian module.

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COPYRIGHT: © Global Science Press

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@Article{CMR-26-230, author = {Chu , Lizhong}, title = {Some Results for Formal Local Cohomology Modules}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {26}, number = {3}, pages = {230--238}, abstract = {

Let $(R, m)$ be a commutative Noetherian local ring, $I$ an ideal of $R$ and $M$ a finitely generated $R$-module. Let $\mathop{\rm lim}\limits_{\mathop{n} \limits ^{\longleftarrow}}H^i_m(M/I^nM)$ be the $i$th formal local cohomology module of $M$ with respect to $I$. In this paper, we discuss some properties of formal local cohomology modules $\mathop{\rm lim}\limits_{\mathop{n} \limits ^{\longleftarrow}}H^i_m(M/I^nM)$, which are analogous to the finiteness and Artinianness of local cohomology modules of a finitely generated module.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19155.html} }
TY - JOUR T1 - Some Results for Formal Local Cohomology Modules AU - Chu , Lizhong JO - Communications in Mathematical Research VL - 3 SP - 230 EP - 238 PY - 2021 DA - 2021/05 SN - 26 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19155.html KW - local cohomology, formal local cohomology, coartinian module, minimax module, Artinian module. AB -

Let $(R, m)$ be a commutative Noetherian local ring, $I$ an ideal of $R$ and $M$ a finitely generated $R$-module. Let $\mathop{\rm lim}\limits_{\mathop{n} \limits ^{\longleftarrow}}H^i_m(M/I^nM)$ be the $i$th formal local cohomology module of $M$ with respect to $I$. In this paper, we discuss some properties of formal local cohomology modules $\mathop{\rm lim}\limits_{\mathop{n} \limits ^{\longleftarrow}}H^i_m(M/I^nM)$, which are analogous to the finiteness and Artinianness of local cohomology modules of a finitely generated module.

Chu , Lizhong. (2021). Some Results for Formal Local Cohomology Modules. Communications in Mathematical Research . 26 (3). 230-238. doi:
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