UPPER BOUNDS FOR FINITENESS OF GENERALIZED LOCAL COHOMOLOGY MODULES
Let $R$ be a commutative Noetherian ring with non-zero identity and $fa$ an ideal of $R$. Let $M$ be a finite $R$--module of finite projective dimension and $N$ an arbitrary finite $R$--module. We characterize the membership of the generalized local cohomology modules $lc^{i}_{fa}(M,N)$ in certain S...
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| Format: | Article |
| Language: | English |
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Shahrood University of Technology
2013-09-01
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| Series: | Journal of Algebraic Systems |
| Subjects: | |
| Online Access: | http://jas.shahroodut.ac.ir/article_169_c37d47751d382a040ab25cdfc4d74ec6.pdf |
| _version_ | 1819211577277022208 |
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| author | Moharram Aghapournahr |
| author_facet | Moharram Aghapournahr |
| author_sort | Moharram Aghapournahr |
| collection | DOAJ |
| description | Let $R$ be a commutative Noetherian ring with non-zero identity and $fa$ an ideal of $R$. Let $M$ be a finite $R$--module of finite projective dimension and $N$ an arbitrary finite $R$--module. We characterize the membership of the generalized local cohomology modules $lc^{i}_{fa}(M,N)$ in certain Serre subcategories of the category of modules from upper bounds. We define and study the properties of a generalization of cohomological dimension of generalized local cohomology modules. Let $mathcal S$ be a Serre subcategory of the category of $R$--modules and $n > pd M$ be an integer such that $lc^{i}_{fa}(M,N)$ belongs to $mathcal S$ for all $i> n$. Then, for any ideal $fbsupseteq fa$, it is also shown that the module $lc^{n}_{fa}(M,N)/{fb}lc^{n}_{fa}(M,N)$ belongs to $mathcal S$. |
| first_indexed | 2024-12-23T06:29:17Z |
| format | Article |
| id | doaj.art-79e382a8ba0842279d62c7dbe6022e39 |
| institution | Directory Open Access Journal |
| issn | 2345-5128 2345-511X |
| language | English |
| last_indexed | 2024-12-23T06:29:17Z |
| publishDate | 2013-09-01 |
| publisher | Shahrood University of Technology |
| record_format | Article |
| series | Journal of Algebraic Systems |
| spelling | doaj.art-79e382a8ba0842279d62c7dbe6022e392022-12-21T17:56:59ZengShahrood University of TechnologyJournal of Algebraic Systems2345-51282345-511X2013-09-01111910.22044/jas.2013.169169UPPER BOUNDS FOR FINITENESS OF GENERALIZED LOCAL COHOMOLOGY MODULESMoharram Aghapournahr0Arak AniversityLet $R$ be a commutative Noetherian ring with non-zero identity and $fa$ an ideal of $R$. Let $M$ be a finite $R$--module of finite projective dimension and $N$ an arbitrary finite $R$--module. We characterize the membership of the generalized local cohomology modules $lc^{i}_{fa}(M,N)$ in certain Serre subcategories of the category of modules from upper bounds. We define and study the properties of a generalization of cohomological dimension of generalized local cohomology modules. Let $mathcal S$ be a Serre subcategory of the category of $R$--modules and $n > pd M$ be an integer such that $lc^{i}_{fa}(M,N)$ belongs to $mathcal S$ for all $i> n$. Then, for any ideal $fbsupseteq fa$, it is also shown that the module $lc^{n}_{fa}(M,N)/{fb}lc^{n}_{fa}(M,N)$ belongs to $mathcal S$.http://jas.shahroodut.ac.ir/article_169_c37d47751d382a040ab25cdfc4d74ec6.pdfGeneralized local cohomology moduleSerre subcategorycohomological dimension |
| spellingShingle | Moharram Aghapournahr UPPER BOUNDS FOR FINITENESS OF GENERALIZED LOCAL COHOMOLOGY MODULES Journal of Algebraic Systems Generalized local cohomology module Serre subcategory cohomological dimension |
| title | UPPER BOUNDS FOR FINITENESS OF GENERALIZED LOCAL COHOMOLOGY
MODULES |
| title_full | UPPER BOUNDS FOR FINITENESS OF GENERALIZED LOCAL COHOMOLOGY
MODULES |
| title_fullStr | UPPER BOUNDS FOR FINITENESS OF GENERALIZED LOCAL COHOMOLOGY
MODULES |
| title_full_unstemmed | UPPER BOUNDS FOR FINITENESS OF GENERALIZED LOCAL COHOMOLOGY
MODULES |
| title_short | UPPER BOUNDS FOR FINITENESS OF GENERALIZED LOCAL COHOMOLOGY
MODULES |
| title_sort | upper bounds for finiteness of generalized local cohomology modules |
| topic | Generalized local cohomology module Serre subcategory cohomological dimension |
| url | http://jas.shahroodut.ac.ir/article_169_c37d47751d382a040ab25cdfc4d74ec6.pdf |
| work_keys_str_mv | AT moharramaghapournahr upperboundsforfinitenessofgeneralizedlocalcohomologymodules |