{"title":"Cofiniteness of local cohomology modules in the class of modules in dimension less than a fixed integer","authors":"A. Vahidi, Mahdieh Papari-Zarei","doi":"10.33044/REVUMA.1786","DOIUrl":null,"url":null,"abstract":". Let n be a non-negative integer, R a commutative Noetherian ring with dim( R ) ≤ n + 2, a an ideal of R , and X an arbitrary R -module. In this paper, we first prove that X is an (FD <n , a )-cofinite R -module if X is an a -torsion R -module such that Hom R (cid:0) R a ,X (cid:1) and Ext 1 R (cid:0) R a ,X (cid:1) are FD <n R -modules. Then, we show that H i a ( X ) is an (FD <n , a )-cofinite R -module and { p ∈ Ass R (H i a ( X )) : dim (cid:0) R p (cid:1) ≥ n } is a finite set for all i when Ext iR (cid:0) R a ,X (cid:1) is an FD <n R -module for all i ≤ n + 2. As a consequence, it follows that Ass R (H i a ( X )) is a finite set for all i whenever R is a semi-local ring with dim( R ) ≤ 3 and X is an FD < 1 R -module. Finally, we observe that the category of (FD <n , a )-cofinite R -modules forms an Abelian subcategory of the category of R -modules.","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":"10 1","pages":"191-198"},"PeriodicalIF":0.6000,"publicationDate":"2021-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Revista De La Union Matematica Argentina","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.33044/REVUMA.1786","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
. Let n be a non-negative integer, R a commutative Noetherian ring with dim( R ) ≤ n + 2, a an ideal of R , and X an arbitrary R -module. In this paper, we first prove that X is an (FD
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Revista de la Unión Matemática Argentina is an open access journal, free of charge for both authors and readers. We publish original research articles in all areas of pure and applied mathematics.
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