Melkersson condition on Serre subcategories

Reza Sazeedeh, and Rasul Rasuli. "Melkersson condition on Serre subcategories." Colloquium Mathematicae 144.2 (2016): 289-300. <http://eudml.org/doc/286303>.

@article{RezaSazeedeh2016,
abstract = {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 $C_\{\}$, 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 $C_\{\}$. If and are ideals of R, we get a necessary and sufficient condition for to satisfy $C_\{\}$ and $C_\{\}$ simultaneously. We also find some sufficient conditions under which satisfies $C_\{\}$. As an application, we investigate when local cohomology modules lie in a Serre subcategory.},
author = {Reza Sazeedeh, Rasul Rasuli},
journal = {Colloquium Mathematicae},
keywords = {Serre subcategory; melkersson condition; local cohomology},
language = {eng},
number = {2},
pages = {289-300},
title = {Melkersson condition on Serre subcategories},
url = {http://eudml.org/doc/286303},
volume = {144},
year = {2016},
}

TY - JOUR
AU - Reza Sazeedeh
AU - Rasul Rasuli
TI - Melkersson condition on Serre subcategories
JO - Colloquium Mathematicae
PY - 2016
VL - 144
IS - 2
SP - 289
EP - 300
AB - 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 $C_{}$, 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 $C_{}$. If and are ideals of R, we get a necessary and sufficient condition for to satisfy $C_{}$ and $C_{}$ simultaneously. We also find some sufficient conditions under which satisfies $C_{}$. As an application, we investigate when local cohomology modules lie in a Serre subcategory.
LA - eng
KW - Serre subcategory; melkersson condition; local cohomology
UR - http://eudml.org/doc/286303
ER -