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On the length of the powers of systems of parameters in local ring

Published online by Cambridge University Press:  22 January 2016

Nguyen Tu Cuong
Nguyen Tu Cuong*
Affiliation:
Institute of Mathematics, P.O. Box 631, Bo Ho, Hanoi, Vietnam
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Throughout this note, A denotes a commutative local Noetherian ring with maximal ideal m and M a finitely generated A-module with dim (M) = d. Let x1, …, xd be a system of parameters (s.o.p. for short) for M and I the ideal of A generated by x1, …, xd.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 120 , December 1990 , pp. 77 - 88
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1990

References

[1] Auslander, M. and Buchsbaum, D. A., Codimension and multiplicity, Ann. Math., 68 (1958), 625–657.Google Scholar
[2] Brodmann, M., Kohomologische Eigenschaften von Aufblasungen an lokalen vollständigen Durchschnitten, Habilitationsschrift, Münster 1980.Google Scholar
[3] Cuong, N. T., Trung, N. V. and Schenzel, P., Verallgemeinerte Cohen-Macaulay Moduln, Math. Nachr., 85 (1978), 57–73.Google Scholar
[4] Ferrand, D. and Raynaud, M., Fibres formelles d’un anneau local Noetherien, Ann. Sc. Ecole Norm. Sup., 3 (1970), 295–311.CrossRefGoogle Scholar
[5] Garcia Roig, J-L and Kirby, D., On the Koszul homology modules for the powers of a multiplicity system, Mathematika, 33 (1986), 96–101.CrossRefGoogle Scholar
[6] Schenzel, P., Finiteness of relative Rees ring and Asymptotic Prime Divisor, Math. Nachr., 129 (1986), 123–148.CrossRefGoogle Scholar
[7] Serre, J-P., Algèbre locale: Multiplicités, Lecture Notes in Math. No. 11, 1965.Google Scholar
[8] Stückrad, J. and Vogel, W., Eine Verallgemeinerung der Cohen-Macaulay Ringe und Anwendungen auf ein Problem der Multiplizitätstheorie, J. Math. Kyoto Univ., 13 (1973), 513–528.Google Scholar
[9] Sharp, R. Y. and Hamieh, M. A., Lengths of certain generalized fraction, J. pure Appl. Algebra, 38 (1985), 323–336.Google Scholar
[10] Trung, N. V., Absolutely superficial sequence, Math. Proc. Cambrige Phil. Soc., 93 (1983), 35–47.Google Scholar
[11] Trung, N. V., Toward a theory of generalized Cohen Macaulay modules, Nagoya Math. J., 102 (1986), 1–49.Google Scholar
[12] Cuong, N. T., Generalized Cohen-Macaulay modules with non-Cohen-Macaulay locus of positive dimension, preprint.Google Scholar
[13] Huneke, C., Theory of d-sequenees and powers of ideals, Adv. in Math., 46 (1982), 249–279.CrossRefGoogle Scholar