TY - JOUR
A2 - Jaballah, Ali
AU - Hassani, Feysal
AU - Rasuli, Rasul
PY - 2017
DA - 2017/07/03
TI - Some Properties of Serre Subcategories in the Graded Local Cohomology Modules
SP - 5230589
VL - 2017
AB - Let R=⊕n≥0Rn be a standard homogeneous Noetherian ring with local base ring (R0,m0) and let M be a finitely generated graded R-module. Let HR+i(M) be the ith local cohomology module of M with respect to R+=⊕n>0Rn. Let S be a Serre subcategory of the category of R-modules and let i be a nonnegative integer. In this paper, if dimR0≤1, then we investigate some conditions under which the R-modules R0/m0 ⊗R0 HR+i(M),Γm0R(HR+i(M)) and Hm0R1(HR+i(M)) are in S for all i≥0. Also, we prove that if dimR0≤2, then the graded R-module Hm01(HR+i(M)) is in S for all i≥0. Finally, we prove that if n is the biggest integer such that Hai(M)∉S, then HR+i(M)/m0HR+i(M)∈S for all i≥n.
SN - 2314-4629
UR - https://doi.org/10.1155/2017/5230589
DO - 10.1155/2017/5230589
JF - Journal of Mathematics
PB - Hindawi
KW -
ER -