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Counterexample to the paper “On the Gorenstein injective dimension and Bass formula”

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In this note, we give a counterexample for Theorem 2.3 of the above mentioned paper that is a generalization of the Grothendieck non-vanishing theorem to a class of modules larger than finitely generated modules.

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References

  • M. Aghapournahr and L. Melkersson, On the vanishing, Artinianness and finiteness of local cohomology modules, arXive:0903.2235v1 [math AC].

  • M. P. Brodmann and R. Y. Sharp, Local cohomology: an algebraic introduction with geometric applications, Cambridge University Press, 1998.

  • W. Bruns and J. Herzog, Cohen-Macaulay rings, Cambridge University Press, revised ed., 1998.

  • C. Huneke, Problems on local cohomology: Free resolutions in commutative algebra and algebraic geometry, (Sundance, UT, 1990), 93–108, Jones and Bartlett, 1992.

  • Khosh-Ahang F.: On the Gorenstein injective dimension and Bass formula. Arch. Math. 90, 18–23 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  • Mafi A.: Some results on the local cohomology modules. Arch. Math. 87, 211–216 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  • Matsumura H.: Commutative ring theory, Cambridge University Press, 1986.

  • Rudlof P.: On minimax and related modules. Can. J. Math. 44, 154–166 (1992)

    MATH  MathSciNet  Google Scholar 

  • Zink T.: Endlichkeitsbedingungen für Moduln über einem Noetherschen Ring. Math. Nachr. 164, 239–252 (1974)

    Article  MathSciNet  Google Scholar 

  • Zöschinger H.: Koatomare Moduln. Math. Z. 170, 221–232 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  • Zöschinger H.: Minimax Moduln. J. Algebra. 102, 1–32 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  • Zöschinger H.: Über die Maximalbedingung für radikalvolle Untermoduln. Hokkaido Math. J. 17, 101–116 (1988)

    MATH  MathSciNet  Google Scholar 

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Correspondence to Moharram Aghapournahr.

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Aghapournahr, M. Counterexample to the paper “On the Gorenstein injective dimension and Bass formula”. Arch. Math. 93, 319–321 (2009). https://doi.org/10.1007/s00013-009-0053-0

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  • DOI: https://doi.org/10.1007/s00013-009-0053-0

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