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

 

The f-depth of an ideal on a module


Authors: Rencai Lü and Zhongming Tang
Journal: Proc. Amer. Math. Soc. 130 (2002), 1905-1912
MSC (2000): Primary 13C15, 13D45, 14B15
Published electronically: December 27, 2001
MathSciNet review: 1896021
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Abstract: Let $I$ be an ideal of a Noetherian local ring $R$ and $M$ a finitely generated $R$-module. The f-depth of $I$ on $M$ is the least integer $r$ such that the local cohomology module $H^r_I(M)$ is not Artinian. This paper presents some part of the theory of f-depth including characterizations of f-depth and a relation between f-depth and f-modules.


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Additional Information

Rencai Lü
Affiliation: Department of mathematics, Suzhou University, Suzhou 215006, People’s Republic of China

Zhongming Tang
Affiliation: Department of mathematics, Suzhou University, Suzhou 215006, People’s Republic of China
Email: zmtang@suda.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06269-4
PII: S 0002-9939(01)06269-4
Keywords: f-depth, f-modules, local cohomology modules
Received by editor(s): July 26, 2000
Received by editor(s) in revised form: January 16, 2001
Published electronically: December 27, 2001
Additional Notes: This work was supported by the National Natural Science Foundation of China.
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 2001 American Mathematical Society