On Faltings' local-global principle of generalized local cohomology modules
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- Hoang Nguyen Van
- Thai Nguyen University of Education
Description
Let R be a commutative Noetherian ring, I an ideal of R and M, N finitely generated R-modules. Let 0 ≤ n ∈ Z. This note shows that the least integer i such that dim Supp($H^i_I$(M, N)/K) ≥ n for any finitely generated submodule K of $H^i_I$(M, N) equal to the number inf{fI<sub>$\frak{p}$</sub> (M$\frak{p}$,N$\frak{p}$)|$\frak{p}$ ∈ Supp(N/IMN), dim R/$\frak{p}$ ≥ n}, where fI<sub>$\frak{p}$</sub>(M$\frak{p}$,N$\frak{p}$) is the least integer i such that $H^i_{I_{\frak{p}}} (M$\frak{p}$,N$\frak{p}$) is not finitely generated, and IM = ann(M/IM). This extends the main result of Asadollahi-Naghipour [1] and Mehrvarz-Naghipour-Sedghi [8] for generalized local cohomology modules by a short proof.
Journal
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- Kodai Mathematical Journal
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Kodai Mathematical Journal 40 (1), 58-62, 2017
Department of Mathematics, Tokyo Institute of Technology
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Details 詳細情報について
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- CRID
- 1390282680252798976
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- NII Article ID
- 130005509846
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- ISSN
- 18815472
- 03865991
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- Text Lang
- en
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- Data Source
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- JaLC
- Crossref
- CiNii Articles
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- Abstract License Flag
- Disallowed
