A Finiteness Result for Co-Associated and Associated Primes of Generalized Local Homology and Cohomology Modules

2009 ◽  
Vol 37 (5) ◽  
pp. 1748-1757 ◽  
Author(s):  
Tran Tuan Nam
Keyword(s):  
Associated Primes ◽  
Local Homology ◽  
Finiteness Result ◽  
Cohomology Modules

COFINITENESS OF GENERALIZED LOCAL COHOMOLOGY MODULES

2011 ◽  
Vol 83 (3) ◽  
pp. 382-388 ◽  
Author(s):  
KEIVAN BORNA ◽  
PARVIZ SAHANDI ◽  
SIAMAK YASSEMI
Keyword(s):  
Recent Result ◽  
Nonnegative Integer ◽  
Noetherian Ring ◽  
Local Cohomology ◽  
Associated Primes ◽  
Local Cohomology Modules ◽  
Finiteness Result ◽  
Generalized Local Cohomology Modules ◽  
Cohomology Modules

AbstractLet 𝔞 be an ideal of a Noetherian ring R. Let s be a nonnegative integer and let M and N be two R-modules such that ExtjR(M/𝔞M,Hi𝔞(N)) is finite for all i<s and all j≥0 . We show that HomR (R/𝔞,Hs𝔞(M,N)) is finite provided ExtsR(M/𝔞M,N) is a finite R-module. In addition, for finite R-modules M and N, we prove that if Hi𝔞(M,N) is minimax for all i<s, then HomR (R/𝔞,Hs𝔞(M,N)) is finite. These are two generalizations of the result of Brodmann and Lashgari [‘A finiteness result for associated primes of local cohomology modules’, Proc. Amer. Math. Soc. 128 (2000), 2851–2853] and a recent result due to Chu [‘Cofiniteness and finiteness of generalized local cohomology modules’, Bull. Aust. Math. Soc. 80 (2009), 244–250]. We also introduce a generalization of the concept of cofiniteness and recover some results for it.

On the associated primes of local cohomology modules

1999 ◽  
Vol 27 (12) ◽  
pp. 6191-6198 ◽  
Author(s):  
K. Khashyarmanesh ◽  
Sh Salarian
Keyword(s):  
Local Cohomology ◽  
Associated Primes ◽  
Local Cohomology Modules ◽  
Cohomology Modules

Some properties of local homology and local cohomology modules

2013 ◽  
Vol 50 (1) ◽  
pp. 129-141
Author(s):  
Tran Nam
Keyword(s):  
Local Cohomology ◽  
Local Homology ◽  
Local Cohomology Modules ◽  
Cohomology Modules ◽  
Compact Module

We study some properties of representable or I-stable local homology modules HiI (M) where M is a linearly compact module. By duality, we get some properties of good or at local cohomology modules HIi (M) of A. Grothendieck.

scholarly journals Local cohomology modules of a smooth $\mathbb{Z}$ -algebra have finitely many associated primes

2013 ◽  
Vol 197 (3) ◽  
pp. 509-519 ◽  
Author(s):  
Bhargav Bhatt ◽  
Manuel Blickle ◽  
Gennady Lyubeznik ◽  
Anurag K. Singh ◽  
Wenliang Zhang
Keyword(s):  
Local Cohomology ◽  
Associated Primes ◽  
Local Cohomology Modules ◽  
Cohomology Modules

scholarly journals On the asymptotic behaviour of associated primes of generalized local cohomology modules

2007 ◽  
Vol 83 (2) ◽  
pp. 217-226 ◽  
Author(s):  
Kazem Khashyarmaneshs ◽  
Ahmad Abbasi
Keyword(s):  
Asymptotic Behavior ◽  
Local Cohomology ◽  
Associated Primes ◽  
Finitely Generated ◽  
Local Cohomology Module ◽  
Commutative Noetherian Ring ◽  
Graded Modules ◽  
Local Cohomology Modules ◽  
Generalized Local Cohomology Modules ◽  
Cohomology Modules

AbstractLetMandNbe finitely generated and graded modules over a standard positive graded commutative Noetherian ringR, with irrelevant idealR+. Letbe thenth component of the graded generalized local cohomology module. In this paper we study the asymptotic behavior of AssfR+() as n → –∞ wheneverkis the least integerjfor which the ordinary local cohomology moduleis not finitely generated.

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