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On the Finiteness of Formal Local Cohomology Modules | Synapse

June 14, 2026Open Access

On the Finiteness of Formal Local Cohomology Modules

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. (Fri,) studied this question.

synapsesocial.com/papers/6a2e472bb1cc60ccdea8bca7 https://doi.org/https://doi.org/10.22044/jas.2022.11072.1549

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