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    Eghbali, Majid and Schenzel, Peter 2012. On an Endomorphism Ring of Local Cohomology. Communications in Algebra, Vol. 40, Issue. 11, p. 4295.

    Nhan, Le Thanh and Chau, Tran Do Minh 2012. On the top local cohomology modules. Journal of Algebra, Vol. 349, Issue. 1, p. 342.

    Divaani-Aazar, Kamran and Hajikarimi, Alireza 2011. Generalized Local Cohomology Modules and Homological Gorenstein Dimensions. Communications in Algebra, Vol. 39, Issue. 6, p. 2051.

    Divaani-Aazar, Kamran 2009. Vanishing of the top local cohomology modules over Noetherian rings. Proceedings - Mathematical Sciences, Vol. 119, Issue. 1, p. 23.

    Tousi, Massoud and Yassemi, Siamak 2008. The Lichtenbaum–Hartshorne theorem for modules which are finite over a ring homomorphism. Journal of Pure and Applied Algebra, Vol. 212, Issue. 5, p. 1222.

    Khashyarmanesh, Kazem 2005. A SURJECTIVE HOMOMORPHISM OF LOCAL COHOMOLOGY MODULES. Communications in Algebra, Vol. 33, Issue. 8, p. 2717.

    Sazeedeh, Reza 2005. STRONGLY TORSION-FREE MODULES AND LOCAL COHOMOLOGY OVER COHEN–MACAULAY RINGS. Communications in Algebra, Vol. 33, Issue. 4, p. 1127.

  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 131, Issue 2
  • September 2001, pp. 211-226

Ideal topologies, local cohomology and connectedness

  • K. DIVAANI-AAZAR (a1) and P. SCHENZEL (a2)
  • DOI:
  • Published online: 26 October 2001

Let [afr ] be an ideal of a local ring (R, [mfr ]) and let N be a finitely generated R-module of dimension d: It is shown that Hd[afr ](N) ≃ Hd[mfr ](N)/[sum ]n∈ℕ〈[mfr ]〉 (0: Hd[mfr ](N)[afr ]n); where for an Artinian R-module X we put 〈[mfr ]〉X = ∩n∈ℕ[mfr ]nX. As a consequence several vanishing and connectedness results are deduced.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
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