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- Title
Tameness and Artinianness of Graded Generalized Local Cohomology Modules.
- Authors
Jahangiri, M.; Shirmohammadi, N.; Tahamtan, Sh.
- Abstract
Let R=⊕n ≥ 0 Rn be a standard graded ring, 픞 ⊇ ⊕n > 0 Rn an ideal of R, and M, N two finitely generated graded R-modules. This paper studies the homogeneous components of graded generalized local cohomology modules. We show that for any i ≥ 0, the n-th graded component of the i-th generalized local cohomology module of M and N with respect to 픞 vanishes for all n ≫ 0. Some sufficient conditions are proposed to satisfy the equality . Also, some sufficient conditions are proposed for the tameness of such that or i=픞(M,N), where and 픞(M,N) denote the R+-finiteness dimension and the cohomological dimension of M and N with respect to 픞, respectively. Finally, we consider the Artinian property of some submodules and quotient modules of , where j is the first or last non-minimax level of .
- Subjects
GENERALIZATION; COHOMOLOGY theory; MODULES (Algebra); LOCAL rings (Algebra); RING theory; FINITE rings
- Publication
Algebra Colloquium, 2015, Vol 22, Issue 1, p131
- ISSN
1005-3867
- Publication type
Article
- DOI
10.1142/S1005386715000127