A+ CATEGORY SCIENTIFIC UNIT

A new version of Local-Global Principle for annihilations of local cohomology modules

Volume 100 / 2004

K. Khashyarmanesh, M. Yassi, A. Abbasi Colloquium Mathematicum 100 (2004), 213-219 MSC: 13D45, 13E5. DOI: 10.4064/cm100-2-5

Abstract

Let $R$ 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.

Authors

  • K. KhashyarmaneshInstitute for Studies in
    Theoretical Physics and Mathematics
    P.O. Box 19395-5746
    Tehran, Iran
    e-mail
  • M. YassiDepartment of Mathematics
    Mashhad University
    P.O. Box 1159-91775
    Mashhad, Iran
  • A. AbbasiDepartment of Mathematics
    Mashhad University
    P.O. Box 1159-91775
    Mashhad, Iran
    e-mail

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