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- W2963391627 abstract "Let $R$ be a commutative noetherian ring, let $frak a$ and $frak b$ be two ideals of $R$; and let $Ss$ be a Serre subcategory of $R$-modules. We give a necessary and sufficient condition by which $Ss$ satisfies $C_{frak a}$ and $C_{frak b}$ conditions. As an conclusion we show that over a artinian local ring, every Serre subcategory satisfies $C_{frak a}$ condition. We also show that $Ss_{frak a}$ is closed under extension of modules. If $Ss$ is a torsion subcategory, we prove that $S$ satisfies $C_{frak a}$ condition. We prove that $C_{frak a}$ condition can be transferred via rings homomorphism. As some applications, we give several results concerning with Serre subcategories in local cohomology theory." @default.
- W2963391627 created "2019-07-30" @default.
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- W2963391627 date "2016-01-01" @default.
- W2963391627 modified "2023-10-16" @default.
- W2963391627 title "Melkersson condition on Serre subcategories" @default.
- W2963391627 doi "https://doi.org/10.4064/cm6384-9-2015" @default.
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