Volume 9, Issue 3 (12-2023)
mmr 2023, 9(3): 136-146 |
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Rezaei S. Attached primes of top local cohomology modules. mmr 2023; 9 (3) :136-146
URL: http://mmr.khu.ac.ir/article-1-3200-en.html
URL: http://mmr.khu.ac.ir/article-1-3200-en.html
PNU , sha.Rezaei@gmail.com
Abstract: (592 Views)
Introduction
Leta R M , N R i ≥0 M , N a
H a i M , N ≔ n H a i ( M / a n M , N ).
Also, recall thatcd a , M , N , a R
sup i ∈ N 0 : H a i M , N ≠0 .
An important problem concerning local cohomology is determining the set of attached prime ideals of the top local cohomology modules. This problem has been studied by several authors. In this paper, we study attached prime ideals of top local cohomology modules.
Material and methods
In this paper, we first obtain some subsets of the set of attached prime ideals of top local cohomology module. By using these, we obtain a result about finiteness of top local cohomology modules.
Results and discussion
LetR a R M N R pd M = d <∞ cd a , N = c <∞ .
i ) p ∈ Supp R N : cd a , R / p = c , R p = c ⊆ Att R ( H a c N ) ,
ii ) Att R ( H a d + c M , N ) ⊆ p ∈ Supp R N : cd a , M , R / p = d + c ,
iii ) p ∈ Sup p R N : cd a , M , R p = d + c , R p = c Att R ( H a d + c M , N ) .
Conclusion
LetM N R pd M = d <∞ cd a , N = c <∞ .
• If( R , m ) H a d + c M , N ≠0 H a d + c M , N
• If R is a Noetherian domain, then under certain conditions we have
Att R ( H a d + c M , N ) = Att R ( H a c N )
Let
Also, recall that
An important problem concerning local cohomology is determining the set of attached prime ideals of the top local cohomology modules. This problem has been studied by several authors. In this paper, we study attached prime ideals of top local cohomology modules.
Material and methods
In this paper, we first obtain some subsets of the set of attached prime ideals of top local cohomology module. By using these, we obtain a result about finiteness of top local cohomology modules.
Results and discussion
Let
Conclusion
Let
• If
• If R is a Noetherian domain, then under certain conditions we have
Keywords: local cohomology modules, attached primes
Type of Study: Original Manuscript |
Subject:
alg
Received: 2021/05/26 | Revised: 2024/02/19 | Accepted: 2022/04/22 | Published: 2023/12/31 | ePublished: 2023/12/31
Received: 2021/05/26 | Revised: 2024/02/19 | Accepted: 2022/04/22 | Published: 2023/12/31 | ePublished: 2023/12/31
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