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On Minimax Modules and Generalized Local Cohomology with Respect to a Pair of Ideals

Abstract

We study the minimax properties and the artinianness of the generalized local cohomology modules \(H^{i}_{I,J}(M,N)\) with respect to a pair of ideals (I,J). We also show some results on top generalized local cohomology modules.

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Acknowledgments

The authors are deeply grateful to the referee for careful reading of the paper and for the helpful suggestions. The final work of this paper was done when the second author and the third author visited Vietnam Institute for Advanced Study in Mathematics (VIASM). We would like to thank VIASM for hospitality.

Funding

We received financial support from VIASM. This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No. 101.04-2018.304.

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Correspondence to Tran Tuan Nam.

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Nam, N.T., Nam, T.T. & Tri, N.M. On Minimax Modules and Generalized Local Cohomology with Respect to a Pair of Ideals. Acta Math Vietnam 46, 457–470 (2021). https://doi.org/10.1007/s40306-020-00393-z

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Keywords

  • Attached primes
  • Generalized local cohomology
  • Minimax

Mathematics Subject Classification (2010)

  • 13D45