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Paper   IPM / M / 2319
School of Mathematics
  Title:   Filter regular sequences and generalized local cohomology modules
1.  K. Khashyarmanesh
2.  M. Yassi
3.  A. Abbasi
  Status:   Published
  Journal: Comm. Algebra
  Vol.:  32
  Year:  2004
  Pages:   253-259
  Supported by:  IPM
Let \fraka be an ideal of a commutative Noetherian ring R and let M,N be finitely generated R-modules. We prove that whenever n is a positive integer such that
(i) H\frakan(N) has a finitely many associated prime ideals; and,
(ii) ExtRni (M, H\frakai(N)) is finitely generated for all i=1,2,…, n−1
then the set of associated prime ideals of generalized local cohomology module H\frakan (M,N) is finite. As a consequence, we provide some sufficient conditions for finiteness of AssRHn\fraka (M,N). Also, we show that if M has finite projective dimension d then H\frakan+d (M,N) ≅ H\frakad (M, Hn(a1,…, an) (N)) for any positive integer n and any \fraka-filter regular sequence a1,…, an on N.

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