TY - JOUR
T1 - Tame Loci of Generalized Local Cohomology Modules
TT -
JF - IJMSI
JO - IJMSI
VL - 16
IS - 1
UR - http://ijmsi.ir/article-1-1079-en.html
Y1 - 2021
SP - 169
EP - 180
KW - Graded modules
KW - Generalized local cohomology modules
KW - Associated prime ideals
KW - Tame loci.
N2 - Let $M$ and $N$ be two finitely generated graded modules over a standard graded Noetherian ring $R=bigoplus_{ngeq 0} R_n$. In this paper we show that if $R_{0}$ is semi-local of dimension $leq 2$ then, the set $hbox{Ass}_{R_{0}}Big(H^{i}_{R_{+}}(M,N)_{n}Big)$ is asymptotically stable for $nrightarrow -infty$ in some special cases. Also, we study the torsion-freeness of graded generalized local cohomology modules $H^{i}_{R_{+}}(M,N)$. Finally, the tame loci $T^{i}(M,N)$ of $(M,N)$ will be considered and some sufficient conditions are proposed for the openness of these sets in the Zariski topology.
M3
ER -