Let R be a commutative noetherian ring, let be an ideal of R, and let be a subcategory of the category of R-modules. The condition , defined for R-modules, was introduced by Aghapournahr and Melkersson (2008) in order to study when the local cohomology modules relative to belong to . In this paper, we define and study the class consisting of all modules satisfying . If and are ideals of R, we get a necessary and sufficient condition for to satisfy and simultaneously. We also find some sufficient conditions under which satisfies . As an application, we investigate when local cohomology modules lie in a Serre subcategory.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm6384-9-2015,
author = {Reza Sazeedeh and Rasul Rasuli},
title = {Melkersson condition on Serre subcategories},
journal = {Colloquium Mathematicae},
volume = {144},
year = {2016},
pages = {289-300},
zbl = {06575006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm6384-9-2015}
}
Reza Sazeedeh; Rasul Rasuli. Melkersson condition on Serre subcategories. Colloquium Mathematicae, Tome 144 (2016) pp. 289-300. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm6384-9-2015/