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2016 | 36 | 1 | 15-23
Tytuł artykułu

On the associated prime ideals of local cohomology modules defined by a pair of ideals

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EN
Let I and J be two ideals of a commutative Noetherian ring R and M be an R-module. For a non-negative integer n it is shown that, if the sets $Ass_{R}(Ext^{n}_{R}(R/I,M))$ and $Supp_{R}(Ext^{i}_{R}(R/I,H^{j}_{I,J}(M)))$ are finite for all i ≤ n+1 and all j < n, then so is $Ass_{R}(Hom_{R}(R/I,H^{n}_{I,J}(M)))$. We also study the finiteness of $Ass_{R}(Ext^{i}_{R}(R/I,H^{n}_{I,J}(M)))$ for i = 1,2.
Twórcy
  • Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran
  • School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran
  • Payame Noor University, P.O. Box 19395-3697, Tehran, Iran
  • Payame Noor University, P.O. Box 19395-3697, Tehran, Iran
Bibliografia
  • [1] M. Aghapournahr, Kh. Ahmadi-Amoli and M.Y. Sadeghi, The concept of (I,J)-cohen Macaulay modules, J. Algebraic Syst. 3 (1) (2015), 1-10.
  • [2] N. Bourbaki, Commutative Algebra, Translated from French (Hermann, Paris, 1972).
  • [3] M. Brodmann, Asymptotic behaviour of cohomology: tameness,supports and associated primes, S. Ghorpade, H. Srinivasan, J. Verma (Eds.), 'Commutative Algebra and Algebraic Geometry' Proceedings, Joint International Meeting of the AMS and the IMS on Commutative Algebra and Algebraic Geometry, Bangalore/India, December 17-20, 2003, Contemporary Mathematics 390 (2005) 31-61. doi: 10.1090/conm/390/07292
  • [4] M.P. Brodmann and A. Lashgari Faghani, A finiteness result for associated primes of local cohomology modules, Proc. Amer. Math. Soc. 128 (10) (2000), 2851-2853. doi: 10.1090/S0002-9939-00-05328-4
  • [5] M.P. Brodmann and R.Y. Sharp, Local cohomology: An algebraic introduction with geometric applications (Cambridge University Press, 1998). doi: 10.1017/CBO9780511629204
  • [6] W. Bruns and J. Herzog, Cohen-Macaulay Rings (Cambridge University Press, revised ed., 1998). doi: 10.1017/CBO9780511608681
  • [7] L. Chu, Top local cohomology modules with respect to a pair of ideals, Proc. Amer. Math. Soc. 139 (2011), 777-782. doi: 10.1090/S0002-9939-2010-10471-9
  • [8] L. Chu and Q. Wang, Some results on local cohomology modules defined by a pair of ideals, J. Math. Kyoto Univ. bf 49 (2009), 193-200.
  • [9] R. Hartshorne, Affine duality and cofiniteness, Invent. Math. 9 (1970), 145-164. doi: 10.1007/BF01404554
  • [10] C. Huneke, Free resolutions in commutative algebra and algebraic geometry, Res. Notes Math. 2, Jones and Bartlett (Boston, MA, 1992), 93-108.
  • [11] J. Rotman, An Introduction to Homological Algebra (Academic Press, Second Edition, 2009). doi: 10.1007/b98977
  • [12] P. Schenzel, Explicit computations around the Lichtenbaum-Hartshorne vanishing theorem, Manuscripta Math. 78 (1) (1993), 57-68. doi: 10.1007/BF02599300
  • [13] A. Singh, P-torsion elements in local cohomology modules (English summary), Math. Res. Lett. 7 (2000), 165-176. doi: 10.4310/MRL.2000.v7.n2.a3
  • [14] R. Takahashi, Y. Yoshino and T. Yoshizawa, Local cohomology based on a nonclosed support defined by a pair of ideals, J. Pure Appl. Algebra. 213 (2009), 582-600. doi: 10.1016/j.jpaa.2008.09.008
  • [15] A. Tehranian and A. Pour Eshmanan Talemi, Cofinitness of local cohomology based on a non-closed spport defiend by a pair of ideals, Bull. Iranian Math. Soc. 36 (2) (2010), 145-155.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1244
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