“School of Mathematics”

Back to Papers Home
Back to Papers of School of Mathematics

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
  Abstract:
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.

Download TeX format
back to top
Clients Logo
Clients Logo
Clients Logo
Clients Logo
Clients Logo
Clients Logo
Clients Logo
Clients Logo
scroll left or right