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Dehghani-Zadeh, Fatemeh Korean Mathematical Society 2016 대한수학회논문집 Vol.31 No.4
Let I and J be two ideals of a commutative Noetherian ring R and M, N be two non-zero finitely generated R-modules. Let t be a non-negative integer such that $H^i_{I,J}(N)$ is (I, J)-minimax for all i < t. It is shown that the generalized local cohomology module $H^i_{I,J}(M,N)$ is (I, J)-Cofinite minimax for all i < t. Also, we prove that the R-module $Ext^j_R(R/I,H^i_{I,J}(N))$ is finitely generated for all $i{\leq}t$ and j = 0, 1.
Dehghani-Zadeh, Fatemeh Korean Mathematical Society 2012 대한수학회지 Vol.49 No.6
The membership of the generalized local cohomology modules $H_a^i$(M,N) of two R-modules M and N with respect to an ideal a in certain Serre subcategories of the category of modules is studied from below ($i<t$). Furthermore, the behaviour of the $n$th graded component $H_a^i(M,N)_n$ of the generalized local cohomology modules with respect to an ideal containing the irrelevant ideal as $n{\rightarrow}-{\infty}$ is investigated by using the above result, in certain graded situations.
Fatemeh Dehghani-Zadeh 대한수학회 2012 대한수학회지 Vol.49 No.6
The membership of the generalized local cohomology modules Hi a(M,N) of two R-modules M and N with respect to an ideal a in certain Serre subcategories of the category of modules is studied from below (i < t). Furthermore, the behaviour of the nth graded component Hi a(M,N)n of the generalized local cohomology modules with respect to an ideal containing the irrelevant ideal as n ! −1 is investigated by using the above result, in certain graded situations.
Results of Graded Local Cohomology Modules with respect to a Pair of Ideals
Dehghani-Zadeh, Fatemeh Department of Mathematics 2018 Kyungpook mathematical journal Vol.58 No.1
Let $R ={\oplus}_{n{\in}Z}R_n$ be a graded commutative Noetherian ring and let I be a graded ideal of R and J be an arbitrary ideal. It is shown that the i-th generalized local cohomology module of graded module M with respect to the (I, J), is graded. Also, the asymptotic behaviour of the homogeneous components of $H^i_{I,J}(M)$ is investigated for some i's with a specified property.