ON THE WEAK ARTINIANNESS AND MINIMAX GENERALIZED LOCAL COHOMOLOGY MODULES

Title & Authors
ON THE WEAK ARTINIANNESS AND MINIMAX GENERALIZED LOCAL COHOMOLOGY MODULES
Gu, Yan;

Abstract
Let R be a commutative Noetherian ring, I an ideal of R, M and N two R-modules. We characterize the least integer i such that $\small{H^i_I(M,N)}$ is not weakly Artinian by using the notion of weakly filter regular sequences. Also, a local-global principle for minimax generalized local cohomology modules is shown and the result generalizes the corresponding result for local cohomology modules.
Keywords
generalized local cohomology modules;weak Artinianness;minimax module;
Language
English
Cited by
References
1.
M. Aghapournahr and L. Melkersson, Finiteness properties of minimax and coatomic local cohomology modules, Arch. Math. 94 (2010), no. 6, 519-528.

2.
J. Asadollahi, K. Khashyarmanesh, and Sh. Salarian, On the finiteness properties of the generalized local cohomology modules, Comm. Algebra 30 (2002), no. 2, 859-867.

3.
M. P. Brodmann and R. Y. Sharp, Local Cohomology: An Algebraic Introduction with Geometric Applications, Cambridge Studies in Advanced Mathematics, 60. Cambridge University Press, 1998.

4.
L. Z. Chu and Z. M. Tang, On the artinianness of generalized local cohomology, Comm. Algebra 35 (2007), no. 12, 3821-3827.

5.
K. Divaani-Aazar and A. Mafi, Associated primes of local cohomology modules, Proc. Amer. Math. Soc. 133 (2005), no. 3, 655-660.

6.
A. Hajikarimi, Local cohomology modules which are supported only at finitely many maximal ideals, J. Korean Math. Soc. 47 (2010), no. 3, 633-643.

7.
J. Herzog, Komplex Auflosungen und Dualitat in der lokalen Algebra, Habilitationsschrift, Universitat Regensburg, 1974.

8.
L. Melkersson, Modules cofinite with respect to an ideal, J. Algebra 285 (2005), no. 2, 649-668.

9.
H. Saremi, On minimax and generalized local cohomology modules, Acta Math. Vietnam. 34 (2009), no. 2, 269-273.

10.
P. Schenzel, Proregular sequences, local cohomology, and completion, Math. Scand. 92 (2003), no. 2, 161-180.

11.
A. Tehranian, Finiteness result for generalized local cohomology modules, Taiwanese J. Math 14 (2010), no. 2, 447-451.

12.
H. Zoschinger, Minimax module, J. Algebra 102 (1986), no. 1, 1-32.