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Depth formulas for certain graded rings associated to an ideal

Published online by Cambridge University Press:  22 January 2016

Sam Huckaba and
Thomas Marley
Sam Huckaba
Affiliation:
Department of Mathematics, Florida State University, Tallahassee, FL 32306-3027, U.S.A.
Thomas Marley
Affiliation:
Department of Mathematics, Florida State University, Tallahassee, FL 32306-3027, U.S.A.
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In this paper, we investigate the relationship between the depths of the Rees algebra R[It] and the associated graded ring grI(R) of an ideal I in a local ring (R, m) of dimension d > 0. Here

and

.

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 133 , March 1994, pp. 57 - 69
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1994

References

[Br1] Brodmann, M., Einige Ergebnisse aus der lokalen Kohomologietheorie und ihre Anwendung, Osnabrücker Schrifter zur Mathematik, 5 (1983).Google Scholar
[Br2] Brodmann, M., Local cohomology of certain Rees- and form-rings I, J. Algebra, 81 (1984), 29–57.CrossRefGoogle Scholar
[Br3] Brodmann, M., Local cohomology of certain Rees- and form-rings II, J. Algebra, 86 (1985), 457–493.CrossRefGoogle Scholar
[CST] Cuong, N. T., Schenzel, P. and Trung, N. V., Verallgemeinerte Cohen-Macaulay-Moduln, Math. Nachr., (1978), 57–73.Google Scholar
[F] Faltings, G., Uber die Annulatoren lokaler Kohomologiegruppen, Arch. Math., 30 (1978), 473–476.CrossRefGoogle Scholar
[G] Goto, S., On Buchsbaum rings, J. Algebra, 67 (1980), 272–279.CrossRefGoogle Scholar
[GS1] Goto, S. and Shimoda, Y., On Rees algebras over Buchsbaum rings, J. Math. Kyoto Univ., 20(1980), 691–708.Google Scholar
[GS2] Goto, S. and Shimoda, Y., On the Rees algebra of Cohen-Macaulay local rings, Commutative Algebra: analytical methods, Lecture Notes in Pure and Applied Math., no. 68, Dekker, New York, 1982.Google Scholar
[GW] Goto, S. and Watanabe, K., On graded rings I, J. Math. Soc. Japan, 30 (2) (1978), 179–213.CrossRefGoogle Scholar
[Gr] Grothendieck, A. (notes by Hartshorne, R.), “Local cohomology,” Lect. Notes in Math., 41, Springer-Verlag, Berlin, 1967.Google Scholar
[Ha] Hartshorne, R., “Residues and duality,” Lect. Notes in Math., 20, Springer-Verlag, Berlin, 1966.Google Scholar
[H] Huckaba, S., Reduction numbers for ideals of higher analytic spread, Math. Proc. Cambridge Phil. Soc, 102 (1987), 49–57.CrossRefGoogle Scholar
[HM] Huckaba, S. and Marley, T., Depth properties of Rees algebras and associated graded rings, J. Algebra, 156, (1993) 259–271.CrossRefGoogle Scholar
[Hu] Huneke, C., On the associated graded ring of an ideal, 111. J. Math., 26 (1982), 121–137.Google Scholar
[Mat] Matsumura, H., “Commutative ring theory,” Cambridge University Press, Cambridge, 1980.Google Scholar
[MR] Matijevic, J. and Roberts, P., A conjecture of Nagata on graded Cohen-Macaulay rings, J. Math. Kyoto Univ., 14 (1974), 125–128.Google Scholar
[NR] Northcott, D. G. and Rees, D., Reductions of ideals in local rings, Proc. Cambridge Phil. Soc, 50(1954), 145–158.CrossRefGoogle Scholar
[Schl] Schenzel, P., Einige Anwendungen der lokalen Dualität und verallgemeinerte Cohen-Macaulay-Moduln, Math. Nachr., 69 (1975), 227–242.CrossRefGoogle Scholar
[Sch2] Schenzel, P., Regular sequences in Rees and symmetric algebras I, Manuscripta Math., 35 (1981), 173–193.CrossRefGoogle Scholar
[Sch3] Schenzel, P., Regular sequences in Rees and symmetric algebras II, Manuscripta Math., 35 (1981), 331–341.CrossRefGoogle Scholar
[SV] Stückrad, J. and Vogel, W., “Buchsbaum rings and applications,” Springer-Verlag, Berlin, 1986.Google Scholar
[T1] Trung, N. V., Toward a theory of generalized Cohen-Macaulay modules, Nagoya Math. J., 102(1986), 1–49.CrossRefGoogle Scholar
[T2] Trung, N. V., Reduction exponent and degree bound for the defining equations of graded rings, Proc. Amer. Math. Soc, 101 (2) (1987), 229–236.CrossRefGoogle Scholar
[T1] Trung, N. V. and Ikeda, S., When is the Rees algebra Cohen-Macaulay?, Comm. Algebra, 17 (12) (1989), 2893–2922.CrossRefGoogle Scholar
[V] Valla, G., Certain graded algebras are always Cohen-Macaulay, J. Algebra, 42 (1976), 537–548.CrossRefGoogle Scholar