Some results on top local cohomology modules with respect to a pair of ideals
Let $I$ and $J$ be ideals of a Noetherian local ring $(R,\mathfrak m)$ and let $M$ be a nonzero finitely generated $R$-module. We study the relation between the vanishing of $H_{I,J}^{\dim M}(M)$ and the comparison of certain ideal topologies. Also, we characterize when the integral closure of an id...
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| Format: | Article |
| Language: | English |
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Institute of Mathematics of the Czech Academy of Science
2020-12-01
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| Series: | Mathematica Bohemica |
| Subjects: | |
| Online Access: | http://mb.math.cas.cz/full/145/4/mb145_4_3.pdf |
| _version_ | 1819172119148232704 |
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| author | Saeed Jahandoust Reza Naghipour |
| author_facet | Saeed Jahandoust Reza Naghipour |
| author_sort | Saeed Jahandoust |
| collection | DOAJ |
| description | Let $I$ and $J$ be ideals of a Noetherian local ring $(R,\mathfrak m)$ and let $M$ be a nonzero finitely generated $R$-module. We study the relation between the vanishing of $H_{I,J}^{\dim M}(M)$ and the comparison of certain ideal topologies. Also, we characterize when the integral closure of an ideal relative to the Noetherian $R$-module $M/JM$ is equal to its integral closure relative to the Artinian $R$-module $H_{I,J}^{\dim M}(M)$. |
| first_indexed | 2024-12-22T20:02:07Z |
| format | Article |
| id | doaj.art-4c85961eb1b0474a8b6b026102a16c5f |
| institution | Directory Open Access Journal |
| issn | 0862-7959 2464-7136 |
| language | English |
| last_indexed | 2024-12-22T20:02:07Z |
| publishDate | 2020-12-01 |
| publisher | Institute of Mathematics of the Czech Academy of Science |
| record_format | Article |
| series | Mathematica Bohemica |
| spelling | doaj.art-4c85961eb1b0474a8b6b026102a16c5f2022-12-21T18:14:15ZengInstitute of Mathematics of the Czech Academy of ScienceMathematica Bohemica0862-79592464-71362020-12-01145437738610.21136/MB.2019.0124-18MB.2019.0124-18Some results on top local cohomology modules with respect to a pair of idealsSaeed JahandoustReza NaghipourLet $I$ and $J$ be ideals of a Noetherian local ring $(R,\mathfrak m)$ and let $M$ be a nonzero finitely generated $R$-module. We study the relation between the vanishing of $H_{I,J}^{\dim M}(M)$ and the comparison of certain ideal topologies. Also, we characterize when the integral closure of an ideal relative to the Noetherian $R$-module $M/JM$ is equal to its integral closure relative to the Artinian $R$-module $H_{I,J}^{\dim M}(M)$.http://mb.math.cas.cz/full/145/4/mb145_4_3.pdf artinian module integral closure local cohomology quasi-unmixed module |
| spellingShingle | Saeed Jahandoust Reza Naghipour Some results on top local cohomology modules with respect to a pair of ideals Mathematica Bohemica artinian module integral closure local cohomology quasi-unmixed module |
| title | Some results on top local cohomology modules with respect to a pair of ideals |
| title_full | Some results on top local cohomology modules with respect to a pair of ideals |
| title_fullStr | Some results on top local cohomology modules with respect to a pair of ideals |
| title_full_unstemmed | Some results on top local cohomology modules with respect to a pair of ideals |
| title_short | Some results on top local cohomology modules with respect to a pair of ideals |
| title_sort | some results on top local cohomology modules with respect to a pair of ideals |
| topic | artinian module integral closure local cohomology quasi-unmixed module |
| url | http://mb.math.cas.cz/full/145/4/mb145_4_3.pdf |
| work_keys_str_mv | AT saeedjahandoust someresultsontoplocalcohomologymoduleswithrespecttoapairofideals AT rezanaghipour someresultsontoplocalcohomologymoduleswithrespecttoapairofideals |