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2 results

  • COFINITENESS AND FINITENESS OF GENERALIZED LOCAL COHOMOLOGY MODULES

  • Part of
  • LIZHONG CHU
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 80 / Issue 2 / October 2009
    Published online by Cambridge University Press:
    23 July 2009, pp. 244-250
    Print publication:
    October 2009
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  • Let I be an ideal of a commutative Noetherian local ring R, and M and N two finitely generated modules. Let t be a positive integer. We mainly prove that (i) if HIi(M,N) is Artinian for all i<t, then HIi(M,N) is I-cofinite for all i<t and Hom(R/I,HIt(M,N)) is finitely generated; (ii) if d=pd(M)<∞ and dim N=n<∞, then HId+n(M,N) is I-cofinite. We also prove that if M is a nonzero cyclic R-module, then HIi(N) is finitely generated for all i<t if and only if HIi(M,N) is finitely generated for all i<t.

  • A generalization of the cofiniteness problem in local cohomology modules

  • Part of
  • J. Asadollahi, K. Khashyarmanesh, SH. Salarian
  • Journal:
    Journal of the Australian Mathematical Society / Volume 75 / Issue 3 / December 2003
    Published online by Cambridge University Press:
    09 April 2009, pp. 313-324
    Print publication:
    December 2003
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  • Let R be a commutative Noetherian ring with nonzero identity and let M be a finitely generated R-module. In this paper, we prove that if an ideal I of R is generated by a u.s.d-sequence on M then the local cohomology module (M) is I-cofinite. Furthermore, for any system of ideals Φ of R, we study the cofiniteness problem in the context of general local cohomology modules.