A new version of Local-Global Principle for annihilations of local cohomology modules
Volume 100 / 2004
Colloquium Mathematicum 100 (2004), 213-219
MSC: 13D45, 13E5.
DOI: 10.4064/cm100-2-5
Abstract
Let be a commutative Noetherian ring. Let \mathfrak a and \mathfrak b be ideals of R and let N be a finitely generated R-module. We introduce a generalization of the \mathfrak b-finiteness dimension of f^{\mathfrak b}_{\mathfrak a}(N) relative to \mathfrak a in the context of generalized local cohomology modules as f^{\mathfrak b}_{\mathfrak a}(M,N):= \hbox{inf} \{ i\geq 0\mid {\mathfrak b} \subseteq \sqrt{(0:_R H^i_{\mathfrak a}(M,N))}\,\}, where M is an R-module. We also show that f^{\mathfrak b}_{\mathfrak a}(N)\leq f^{\mathfrak b}_{\mathfrak a}(M,N) for any R-module M. This yields a new version of the Local-Global Principle for annihilation of local cohomology modules. Moreover, we obtain a generalization of the Faltings Lemma.
