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초록· 키워드
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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 $j=0, 1$.
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참고문헌 (14)
참고문헌 신청
M. P. Brodmann / 1998 / Local Cohomology: An Algebraic Introduction with Geometric Applications / Cambridge Univ. Press
F. Dehghani-Zadeh / 2012 / Filter regular sequence and generalized local cohomology with respect to a pair of ideals / J. Math. Ext 6(4):11~19
K. Divaani-Aazar / 2005 / Artinianness of local cohomology modules of ZD-modules / Comm. Algebra 33(8):2857~2863
A. Grothendieck / 1968 / Cohomologie Locale des Faisceaux Coherents et t´eoremes de Lefschetz Locaux et Globaux / SGA2
R. Hartshorne / 1970 / Affine duality and cofiniteness / Invent. Math 9:145~164
F. Dehghani-Zadeh / 2012 / Filter regular sequence and generalized local cohomology with respect to a pair of ideals / J. Math. Ext 6(4):11~19
K. Divaani-Aazar / 2005 / Artinianness of local cohomology modules of ZD-modules / Comm. Algebra 33(8):2857~2863
A. Grothendieck / 1968 / Cohomologie Locale des Faisceaux Coherents et t´eoremes de Lefschetz Locaux et Globaux / SGA2
R. Hartshorne / 1970 / Affine duality and cofiniteness / Invent. Math 9:145~164
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