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ON THE VANISHING OF LOCAL HOMOLOGY MODULES

Published online by Cambridge University Press:  25 February 2013

MARZIYEH HATAMKHANI  and
KAMRAN DIVAANI-AAZAR
MARZIYEH HATAMKHANI
Affiliation:
Department of Mathematics, Az-Zahra University, Vanak, Post Code 19834, Tehran, Iran e-mail: hatamkhanim@yahoo.com
KAMRAN DIVAANI-AAZAR
Affiliation:
Department of Mathematics, Az-Zahra University, Vanak, Post Code 19834, Tehran, Iran, and School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran e-mail: kdivaani@ipm.ir
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Abstract

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Let R be a commutative Noetherian ring, is an ideal of R and M is an R-module. We intend to establish the dual of Grothendieck's Vanishing Theorem for local homology modules. We conjecture that =0 for all i>magRM. We prove this in several cases.

Keywords

13D0713D45
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 55 , Issue 2 , May 2013 , pp. 457 - 464
Copyright
Copyright © Glasgow Mathematical Journal Trust 2013

References

REFERENCES

1.Tarrío, L. Alonso, López, A. Jeremías and Lipman, J., Local homology and cohomology on schemes, Ann. Sci. École Norm. Sup. 30 (1) (Sup. 4) (1997), 1–39.Google Scholar
2.Belshoff, R., Enochs, E. E. and Garcīa Rozas, J. R., Generalized Matlis duality, Proc. Am. Math. Soc. 128 (5) (2000), 1307–1312.Google Scholar
3.Chambless, L., N-Dimension and N-critical modules. Application to Artinian modules, Comm. Algebra 8 (16) (1980), 1561–1592.Google Scholar
4.Cuong, N. T. and Nam, T. T., The I-adic completion and local homology for Artinian modules, Math. Proc. Camb. Philos. Soc. 131 (1) (2001), 61–72.Google Scholar
5.Cuong, N. T. and Nam, T. T., A local homology theory for linearly compact modules, J. Algebra 319 (11) (2008), 4712–4737.CrossRefGoogle Scholar
6.Frankild, A., Vanishing of local homology, Math. Z. 244 (3) (2003), 615–630.CrossRefGoogle Scholar
7.Greenlees, J. P. C. and May, J. P., Derived functors of I-adic completion and local homology, J. Algebra 149 (2) (1992), 438–453.CrossRefGoogle Scholar
8.MacDonald, I. G., Duality over complete local rings, Topology 1 (3) (1962), 213–235.Google Scholar
9.Matlis, E., The Koszul complex and duality, Comm. Algebra 1 (2) (1974), 87–144.CrossRefGoogle Scholar
10.Nagata, M., Local rings, Interscience Tracts in Pure and Applied Mathematics, vol. 13 (Interscience, New York, 1962).Google Scholar
11.Richardson, A. S., Co-localization, co-support and local homology, Rocky Mountain J. Math. 36 (5) (2006), 1679–1703.Google Scholar
12.Roberts, R. N., Krull dimension for Artinian modules over quasi local commutative rings, Quart. J. Math. Oxford Ser., 26 (103) (1975), 269–273.Google Scholar
13.Rudlof, P., On minimax and related modules, Canad. J. Math. 44 (1) (1992), 154–166.Google Scholar
14.Schenzel, P., Proregular sequences, local cohomology, and completion, Math. Scand. 92 (2) (2003), 161–180.Google Scholar
15.Simon, A.-M., Adic-completion and some dual homological results, Publ. Mat. 36 (2B) (1992), 965–979.Google Scholar
16.Simon, A.-M., Some homological properties of complete modules, Math. Proc. Camb. Philos. Soc. 108 (2) (1990), 231–246.Google Scholar
17.Yassemi, S., Magnitude of modules, Comm. Algebra 23 (11) (1995), 3993–4008.Google Scholar
18.Zöschinger, H., Starke Kotorsionsmoduln, Arch. Math. (Basel) 81 (2) (2003), 126–141.Google Scholar
19.Zöschinger, H., Uber koassoziierte primideale, Math. Scand. 63 (2) (1988), 196–211.CrossRefGoogle Scholar
20.Zöschinger, H., Linear-kompakte moduln uber noetherschen ringen, Arch. Math. (Basel) 41 (2) (1983), 121–130.CrossRefGoogle Scholar