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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Top local cohomology modules with respect to a pair of ideals
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by Lizhong Chu PDF
Proc. Amer. Math. Soc. 139 (2011), 777-782 Request permission

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
  • 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
  • © Copyright 2010 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 139 (2011), 777-782
  • MSC (2010): Primary 13D45
  • DOI: https://doi.org/10.1090/S0002-9939-2010-10471-9
  • MathSciNet review: 2745630