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• # Artykuł - szczegóły

## Colloquium Mathematicum

2016 | 144 | 2 | 289-300

## Melkersson condition on Serre subcategories

EN

### Abstrakty

EN
Let R be a commutative noetherian ring, let 𝔞 be an ideal of R, and let 𝓢 be a subcategory of the category of R-modules. The condition $C_{𝔞}$, defined for R-modules, was introduced by Aghapournahr and Melkersson (2008) in order to study when the local cohomology modules relative to 𝔞 belong to 𝓢. In this paper, we define and study the class $𝓢_{𝔞}$ consisting of all modules satisfying $C_{𝔞}$. If 𝔞 and 𝔟 are ideals of R, we get a necessary and sufficient condition for 𝓢 to satisfy $C_{𝔞}$ and $C_{𝔟}$ simultaneously. We also find some sufficient conditions under which 𝓢 satisfies $C_{𝔞}$. As an application, we investigate when local cohomology modules lie in a Serre subcategory.

289-300

wydano
2016

### Twórcy

autor
• Department of Mathematics, Urmia University, P.O. Box 165, Urmia, Iran
• School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran
autor
• Mathematics Department, Faculty of Science, Payame Noor University (PNU), Tehran, Iran