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The research aims to determine when a non-zero Artinian module is I-cofinite based on its structural properties.

June 14, 2026Open Access

Some Results on the Artinian Cofinite Modules

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The research aims to determine when a non-zero Artinian module is I-cofinite based on its structural properties.
Consider a non-zero Artinian R-module M with support in V(I).
Introduce the ideal J and study the relationship between Rad(I0hat{R}^J+Ann_{0hat{R}^J}M) and J0hat{R}^J.
Utilize the properties of J-adic completion of the Noetherian ring R.
M is I-cofinite if and only if Rad(I0hat{R}^J+Ann_{0hat{R}^J}M)=J0hat{R}^J.
Demonstrated the equivalence of the I-cofinite property to conditions on the radical and supports.

Implication

Demonstrates conditions for Artinian modules to be I-cofinite in Noetherian rings, suggesting key properties of module support.

Abstract

Let I be an ideal of a commutative Noetherian ring R and M be a non-zero Artinian R-module with support contained in $V(I)$. In this paper it is shown that M is I-cofinite if and only if Rad(IRJ+Ann_RJM)=JRJ, where J:=∩m∈ Supp Mm and RJ denotes the J-adic comletion of R.

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Cite This Study

Gholamreza Pirmohammadi (2023) studied this question.

synapsesocial.com/papers/6a2e4753b1cc60ccdea8bd43 https://doi.org/10.22044/jas.2022.11608.1588

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Implication

Demonstrates conditions for Artinian modules to be I-cofinite in Noetherian rings, suggesting key properties of module support.

Some Results on the Artinian Cofinite Modules

Key Points

Implication

Abstract

Discussion

Cite This Study

Some Results on the Artinian Cofinite Modules

Key Points

Implication

Abstract

Discussion

Cite This Study

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