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Paper   IPM / M / 8292
School of Mathematics
  Title:   Cohomological dimension of generalized local cohomology modules
  Author(s):  R. Naghipour (Joint with J. Amjadi)
  Status:   Published
  Journal: Algebra Colloq.
  Vol.:  15
  Year:  2008
  Pages:   303 - 308
  Supported by:  IPM
The study of the cohomological dimension of algebraic varieties has produced some interesting results and problems in local algebra. Let \fraka be an ideal of a commutative Noetherian ring R. For finitely generated R-modules M and N, the concept of cohomological dimension cd\frak a(M,N) of M and N with respect to \fraka is introduced. If 0→ N′→ N" → 0 is an exact sequence of finitely generated R-modules, then it is shown that cd\frak a(M,N) = max {cd\fraka(M,N′),cd\fraka(M,N")} whenever proj dim M < ∞. Also, if L is a finitely generated R-module with Supp(N\fraka(N)) ⊆ Supp (L\fraka(L)), then it is proved that cd\fraka(M,N) ≤ max{cd\fraka(M,L),proj dim M}. Finally, as a consequence, a result of Brodmann is improved.

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