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Summary:
It is shown that for any Artinian modules $M$, $\dim M^{\vee }$ is the greatest integer $i$ such that ${\mbox{H}}^i_{\mathfrak m}(M^{\vee })\ne 0$.
References:
[1] A. Grothendick (notes by R. Hartshorne): Local Cohomology. Lecture Notes in Math. 41, Springer Verlag, 1967. MR 0224620
[2] H.-B. Foxby: A homological theory of complexes of modules. Preprint Series No. 19a & 19b, Dept. of Mathematics, Univ. Copenhagen, 1981.
[3] I.G. Macdonald: Secondary representation of modules over a commutative ring. Symp. Math. XI (1973) 23–43. MR 0342506 | Zbl 0271.13001
[4] 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. DOI 10.1093/qmath/23.2.197 | MR 0299598
[5] R.Y. Sharp: Local cohomology theory in commutative algebra. Quart. J. Math. (Oxford) (2) 21 (1970), 425–434. DOI 10.1093/qmath/21.4.425 | MR 0276217 | Zbl 0204.06003
[6] S. Yassemi: Coassociated primes. Comm. Algebra 23 (1995), 1473–1498. DOI 10.1080/00927879508825288 | MR 1317409 | Zbl 0832.13004
[7] S. Yassemi: Magnitude of modules. Comm. Algebra 23 (1995), 3993–4008. DOI 10.1080/00927879508825445 | MR 1351115 | Zbl 0836.13005
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