Melkersson condition on Serre subcategories

2014/04/27 by Reza Sazeedeh, Sazeedeh, Reza, Rasul Rasuli +1
Mathematics · #13C60 #13D45 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13C60 #msc:13D45

paper · pdf · doi:10.48550/arxiv.1404.6711

arxiv created 2014/04/27 · arxiv updated 2014/04/29

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.

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