Melkersson condition on Serre subcategories

• Autorzy: Reza Sazeedeh , Rasul Rasuli
• Języki publikacji: 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.

Kategorie tematyczne

• 13C60: Module categories
• 13D45: Local cohomology

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2016
• Tom: 144
• Numer: 2
• Strony: 289-300

Daty

wydano

2016

Twórcy

autor

Reza Sazeedeh

• 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

Rasul Rasuli

• Mathematics Department, Faculty of Science, Payame Noor University (PNU), Tehran, Iran

Identyfikatory

DOI

10.4064/cm6384-9-2015