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June 14, 20260 citationsOpen Access

On the Finiteness of Formal Local Cohomology Modules

SRShahram RezaeiPayame Noor UniversityMGMahbobeh Gasemi-KalemasihiPayame Noor University

Key Points

  • This research aims to explore the finiteness and minimaxness of formal local cohomology modules associated with an ideal in a local ring.
  • Proving results related to the finiteness and minimaxness of formal local cohomology modules.
  • Investigating properties of the top formal local cohomology FdimM=aMa (M).
  • Determining CosR, AnnR, and AttR for FdimM=aMa (M).
  • The finiteness and minimaxness of the formal local cohomology modules were established.
  • Explicit expressions for CosR(FdimM=aMa (M)), AnnR(FdimM=aMa (M)), and AttR(FdimM=aMa (M)) were determined.

Abstract

Let a be an ideal of local ring (R;m) and M a nitely generated R-module. Inthis paper, we prove some results concerning niteness and minimaxness of formal local cohomologymodules. In particular, we investigate some properties of top formal local cohomologyFdimM=aMa (M) and we determine CosR(FdimM=aMa (M)), AnnR(FdimM=aMa (M)) andAttR(FdimM=aMa (M)).

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Cite This Study

Rezaei et al. (2023) studied this question.

synapsesocial.com/papers/6a2e472bb1cc60ccdea8bca7https://doi.org/10.22044/jas.2022.11072.1549
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