Local cohomology, cofiniteness and homological functors of modules

被引：0
作者：
Kamal Bahmanpour
机构：
[1] University of Mohaghegh Ardabili,Department of Mathematics, Faculty of Sciences
来源：
Czechoslovak Mathematical Journal | 2022年 / 72卷
关键词：
cofinite module; cohomological dimension; ideal transform; local cohomology; Noetherian ring; 13D45; 14B15; 13E05;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Let I be an ideal of a commutative Noetherian ring R. It is shown that the R-modules HIj(M) are I-cofinite for all finitely generated R-modules M and all j ∈ ℕ0 if and only if the R-modules ExtRi (N,HIj(M)) and ToriR (N, HIj(M)) are I-cofinite for all finitely generated R-modules M, N and all integers i, j ∈ ℕ0.
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页码：541 / 558
页数：17
相关论文
共 47 条
[1]  
Abazari R(2011)Cofiniteness of extension functors of cofinite modules J. Algebra 330 507-516
[2]  
Bahmanpour K(2008)Local cohomology and Serre subcategories J. Algebra 320 1275-1287
[3]  
Aghapournahr M(2017)Cohomological dimension, cofiniteness and abelian categories of cofinite modules J. Algebra 484 168-197
[4]  
Melkersson L(2019)A study of cofiniteness through minimal associated primes Commun. Algebra 47 1327-1347
[5]  
Bahmanpour K(2019)Cofiniteness over Noetherian complete local rings Commun. Algebra 47 4575-4585
[6]  
Bahmanpour K(2020)A note on abelian categories of cofinite modules Commun. Algebra 48 254-262
[7]  
Bahmanpour K(2021)On a question of Hartshorne Collect. Math. 72 527-568
[8]  
Bahmanpour K(2009)Cofiniteness of local cohomology modules for ideals of small dimension J. Algebra 321 1997-2011
[9]  
Bahmanpour K(2014)On the category of cofinite modules which is Abelian Proc. Am. Math. Soc. 142 1101-1107
[10]  
Bahmanpour K(2000)Cofiniteness of local cohomology modules over regular local rings Bull. Lond. Math. Soc. 32 1-7
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