{"title":"维数小于固定整数的模类中局部上同模的余性","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":"{\"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}","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}
引用次数: 0
摘要
. 设n为非负整数,R为dim(R)≤n + 2的交换诺瑟环,a为R的理想,X为任意R -模。本文首先证明了如果X是a -扭转R -模,使得hm R (cid:0) R a,X (cid:1)和Ext 1 R (cid:0) R a,X (cid:1)是FD 本文章由计算机程序翻译,如有差异,请以英文原文为准。
Cofiniteness of local cohomology modules in the class of modules in dimension less than a fixed integer
. 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
期刊介绍:
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.