Abstract
It is shown that for any Artinian modules M, M ∨ is the greatest integer i such that \({\text{H}}_m^i \)(M ∨) ≠ 0.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. Grothendick (notes by R. Hartshorne): Local Cohomology. Lecture Notes in Math. 41, Springer Verlag, 1967.
H.-B. Foxby: A homological theory of complexes of modules. Preprint Series No. 19a & 19b, Dept. of Mathematics, Univ. Copenhagen, 1981.
I.G. Macdonald: Secondary representation of modules over a commutative ring. Symp. Math. XI (1973) 23–43.
I. G. Macdonald and R. Y. Sharp: An elementary proof of the non-vanishing of certain local cohomology modules. Quart. J. Math. (Oxford)(2) 23 (1970), 197–204.
R.Y. Sharp: Local cohomology theory in commutative algebra. Quart. J. Math. (Oxford) (2) 21 (1970), 425–434.
S. Yassemi: Coassociated primes. Comm. Algebra 23 (1995), 1473–1498.
S. Yassemi: Magnitude of modules. Comm. Algebra 23 (1995), 3993–4008.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Yassemi, S. On the non-vanishing of local cohomology modules. Czechoslovak Mathematical Journal 47, 585–592 (1997). https://doi.org/10.1023/A:1022858332290
Issue Date:
DOI: https://doi.org/10.1023/A:1022858332290