The f-depth of an ideal on a module
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- by Rencai Lü and Zhongming Tang PDF
- Proc. Amer. Math. Soc. 130 (2002), 1905-1912 Request permission
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.References
- Peter Schenzel, Ngô Viêt Trung, and Nguyễn Tụ’ Cu’ò’ng, Verallgemeinerte Cohen-Macaulay-Moduln, Math. Nachr. 85 (1978), 57–73 (German). MR 517641, DOI 10.1002/mana.19780850106
- Gerd Faltings, Über die Annulatoren lokaler Kohomologiegruppen, Arch. Math. (Basel) 30 (1978), no. 5, 473–476 (German). MR 506246, DOI 10.1007/BF01226087
- Hideyuki Matsumura, Commutative ring theory, Cambridge Studies in Advanced Mathematics, vol. 8, Cambridge University Press, Cambridge, 1986. Translated from the Japanese by M. Reid. MR 879273
- Hermann Kober, Transformationen von algebraischem Typ, Ann. of Math. (2) 40 (1939), 549–559 (German). MR 96, DOI 10.2307/1968939
- R. Y. Sharp, Local cohomology theory in commutative algebra, Quart. J. Math. Oxford Ser. (2) 21 (1970), 425–434. MR 276217, DOI 10.1093/qmath/21.4.425
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
- 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
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 1905-1912
- MSC (2000): Primary 13C15, 13D45, 14B15
- DOI: https://doi.org/10.1090/S0002-9939-01-06269-4
- MathSciNet review: 1896021