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A Splitting Theorem for Local Cohomology and its Applications | | Nguyen Tu Cuong
; Pham Hung Quy
; | | Date: |
18 Sep 2010 | | Abstract: | Let $R$ be a commutative Noetherian ring and $M$ a finitely generated
$R$-module. We show in this paper that, for an integer $t$, if the local
cohomology module $H^{i}_mathfrak{a}(M)$ with respect to an ideal $frak a$ is
finitely generated for all $i<t$, then $$H^{i}_mathfrak{a}(M/xM)cong
H^{i}_mathfrak{a}(M)oplus H^{i+1}_mathfrak{a}(M)$ for all $frak a$-filter
regular elements $x$ containing in a enough large power of $frak a$ and all
$i<t-1$. As consequences we obtain generalizations, by very short proofs, of
the main results of M. Brodmann and A.L. Faghani (A finiteness result for
associated primes of local cohomology modules, Proc. Amer. Math. Soc.,
128(2000), 2851-2853) and of H.L. Truong and the first author (Asymptotic
behavior of parameter ideals in generalized Cohen-Macaulay module, J. Algebra,
320(2008),158-168). | | Source: | arXiv, 1009.3531 | | Services: | Forum | Review | PDF | Favorites | |
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