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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Top local cohomology modules with respect to a pair of ideals


Author: Lizhong Chu
Journal: Proc. Amer. Math. Soc. 139 (2011), 777-782
MSC (2010): Primary 13D45
Published electronically: October 28, 2010
MathSciNet review: 2745630
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Abstract: Let $ (R, {\mathfrak{m}})$ be a commutative Noetherian local ring, and let $ I$ and $ J$ be two proper ideals of $ R$. Let $ M$ be a non-zero finitely generated $ R-$module. We investigate the top local cohomology module $ H_{I,J}^{{\text{dim}}M}(M)$. We get some results about attached prime ideals of the local cohomology module $ H_{I,J}^{{\text{dim}}M}(M)$. As a consequence, we find that there exists a quotient $ L$ of $ M$ such that $ H_{I,J}^{{\text{dim}}M}(M) \cong H_{I}^{{\text{dim}}M}(L)$. Also, we give the generalized version of the Lichtenbaum-Hartshorne Vanishing Theorem for local cohomology modules of a finitely generated module with respect to a pair of ideals.


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Additional Information

Lizhong Chu
Affiliation: Department of Mathematics, Soochow University, 215006, Jiangsu, People’s Republic of China
Email: Chulizhong@suda.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10471-9
PII: S 0002-9939(2010)10471-9
Keywords: Local cohomology modules, vanishing, Artinian modules.
Received by editor(s): April 12, 2009
Received by editor(s) in revised form: March 2, 2010
Published electronically: October 28, 2010
Additional Notes: This work was supported by NSF (10771152, 10926094) of China, by the NSF (09KJB110006) for Colleges and Universities in Jiangsu Province, by the Research Foundation (Q4107805) of Suzhou University and by the Research Foundation of Pre-research Project (Q3107852) of Suzhou University.
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2010 American Mathematical Society