scholarly journals A Note on the Vanishing of Certain Local Cohomology Modules

2012 ◽  
Vol 55 (2) ◽  
pp. 315-318
Author(s):  
M. Hellus
Keyword(s):  
Local Cohomology ◽  
Spectral Sequences ◽  
Local Cohomology Modules ◽  
Finite Module ◽  
Cohomology Modules

AbstractFor a finite module M over a local, equicharacteristic ring (R, m), we show that the well-known formula cd(m,M) = dim M becomes trivial if ones uses Matlis duals of local cohomology modules together with spectral sequences. We also prove a new ring-theoretic vanishing criterion for local cohomology modules.

scholarly journals Artinian and Non-Artinian Local Cohomology Modules

2011 ◽  
Vol 54 (4) ◽  
pp. 619-629 ◽  
Author(s):  
Mohammad T. Dibaei ◽  
Alireza Vahidi
Keyword(s):  
Prime Ideal ◽  
Noetherian Ring ◽  
Maximal Element ◽  
Local Cohomology ◽  
Commutative Noetherian Ring ◽  
Local Cohomology Modules ◽  
Finite Module ◽  
Bass Numbers ◽  
Cohomology Modules

AbstractLet M be a finite module over a commutative noetherian ring R. For ideals a and b of R, the relations between cohomological dimensions of M with respect to a, b, a ⋂ b and a + b are studied. When R is local, it is shown that M is generalized Cohen–Macaulay if there exists an ideal a such that all local cohomology modules of M with respect to a have finite lengths. Also, when r is an integer such that 0 ≤ r < dimR(M), any maximal element q of the non-empty set of ideals ﹛a : (M) is not artinian for some i, i ≥ r} is a prime ideal, and all Bass numbers of (M) are finite for all i ≥ r.

scholarly journals Artinianness of local cohomology modules

2014 ◽  
Vol 52 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Moharram Aghapournahr ◽  
Leif Melkersson
Keyword(s):  
Local Cohomology ◽  
Local Cohomology Modules ◽  
Cohomology Modules

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.

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