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June 14, 20260 citationsOpen Access

On the Cofiniteness of Local Cohomology Modules

GPGholamreza Pirmohammadi

Key Points

  • To determine the cofinite nature of local cohomology modules under certain conditions in Noetherian rings.
  • Assumed an ideal in a commutative Noetherian ring and derived properties of local cohomology modules.
  • Analyzed the cofinite property for local cohomology modules across all finitely generated modules.
  • Demonstrated that local cohomology modules are cofinite for all finitely generated modules in the specified context.
  • Established that if certain modules are cofinite, then all local cohomology modules share this property for any integer index.

Abstract

Suppose that is an ideal of a given commutative Noetherian ring R such that the R-modules H¹_ (M) and H³_ (M) are -cofinite, for every finitely generated R-modules M. In this paper, it is shown that the R-modules Hⁱ_ (M) are -cofinite, for all finitely generated R-modules M and all integers i₀.

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Cite This Study

Gholamreza Pirmohammadi (2026) studied this question.

synapsesocial.com/papers/6a2e4753b1cc60ccdea8bd37https://doi.org/10.22044/jas.2024.14393.1825
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