Cofiniteness of generalized local cohomology modules

Tom 99 / 2004

Kamran Divaani-Aazar, Reza Sazeedeh Colloquium Mathematicum 99 (2004), 283-290 MSC: 13D45, 14B15. DOI: 10.4064/cm99-2-12

Streszczenie

Let ${\mathfrak a}$ denote an ideal of a commutative Noetherian ring $R$, and $M$ and $N$ two finitely generated $R$-modules with $\mathop{\rm pd} M< \infty$. It is shown that if either ${\mathfrak a}$ is principal, or $R$ is complete local and ${\mathfrak a}$ is a prime ideal with $\dim R/{\mathfrak a}=1$, then the generalized local cohomology module $H^i_{{\mathfrak a}}(M,N)$ is $\mathfrak a$-cofinite for all $i \geq 0$. This provides an affirmative answer to a question proposed in [{13}].

Autorzy

  • Kamran Divaani-AazarDepartment of Mathematics
    Az-Zahra University, Vanak
    Tehran 19834, Iran
    and Institute for Studies
    in Theoretical Physics and Mathematics
    P.O. Box 19395-5746, Tehran, Iran
    e-mail
  • Reza SazeedehDepartment of Mathematics
    Uromeiyeh University
    Uromeiyeh, Iran
    and
    Institute of Mathematics
    University for Teacher Education
    599 Taleghani Avenue
    Tehran 15614, Iran

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