Volume 16, Issue 1 (4-2021)                   IJMSI 2021, 16(1): 169-180 | Back to browse issues page

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Dehghani Zadeh F, Jahangiri M. Tame Loci of Generalized Local Cohomology Modules. IJMSI. 2021; 16 (1) :169-180
URL: http://ijmsi.ir/article-1-1079-en.html

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.

Type of Study: Research paper | Subject: Special

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