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On the least degree of polynomials bounding above the differences between lengths and multiplicities of certain systems of parameters in local rings

Published online by Cambridge University Press:  22 January 2016

Nguyen Tu Cuong
Nguyen Tu Cuong*
Affiliation:
Institute of Mathematics, P. O. Box 631 Bó Hô 10.000 Hanoi, Vietnam
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Let A be a commutative local Noetherian ring with the maximal ideal m and M a finitely generated A-module, d = dim M. It is well-known that the difference between the length and the multiplicity of a parameter ideal q of M

gives a lot of informations on the structure of the module M. For instance, M is a Cohen-Macaulay (CM for short) module if and only if IM(q) = 0 for some parameter ideal q or M is Buchsbaum module (see [S-V]) if and only if IM(q) is a constant for all parameter ideals q of M.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 125 , March 1992 , pp. 105 - 114
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1992

References

[A-B] Auslander, M. and Buehsbaum, D. A., Codimension and multiplicity, Ann. Math., 68 (1958), 625–657.CrossRefGoogle Scholar
[C1] Cuong, N. T., On the lengths of the powers of a system of parameters in local ring, Nagoya Math. J., 120 (1990), 77–88.CrossRefGoogle Scholar
[C2] Cuong, N. T., On the dimension of the non- Cohen-Macaulay locus of local rings admitting dualizing complexes, to appear in Math. Proc. Cambridge Phil. Soc, 109 (2) (1991), 479–488.CrossRefGoogle Scholar
[C-S-T] Cuong, N. T., Schenzel, P. and Trung, N. V., Verallgemeinerte Cohen-Macaulay Moduln, Math. Nachr., 85 (1978), 57–73.Google Scholar
[D-E] Daepp, U. and Evans, A., Openness and invariance results on generalized Cohen-Macaulay rings, Houston J. Math., 15 no. 2 (1989), 193–201.Google Scholar
[F-R] Ferrand, D. et Raynaud, M., Fibres formelles d’un anneau local Noetherian, Ann. Sc. Ec. Norm. Sup., (4) 3 (1970), 295–311.Google Scholar
[G] Garcia Roig, J-L., On polynomial bounds for the Koszul homology of certain multiplicity systems, J. London Math. Soc, (2) 34 (1986), 411–416.Google Scholar
[G-K] 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
[M] Matsumura, H., “Commutative algebra”, Second Edition, Benjamin, Reading, 1980.Google Scholar
[N] Nagata, M., “Local rings”, Interscience, New York 1962.Google Scholar
[S] Schenzel, P., Dualisierende Komplexe in der lokalen Algebra und Buchsbaum-Ringe, Lect. Notes in Math. No. 907, Springer-Verlag, Berlin-Heiderberg-New York, 1982 Google Scholar
[S-V] Stückrad, J. and Vogel, W., “Buehsbaum rings and applications”, Springer-Verlag, Berlin-Heidelberg-New York 1986.CrossRefGoogle Scholar