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On the lengths of Koszul homology modules and generalized fractions

  • N. T. Cuong (a1) and N. D. Minh (a1)
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Throughout this paper, let A be a Noetherian local ring with maximal ideal m and M a finitely generated A-module with d = dimAM ≥ 1. Denote by N the set of all positive integers.

Let x = (x1, …, xd) be a system of parameters (s.o.p) for M and let

We consider the following two problems: (i) When is the length of Koszul homology

a polynomial in n for all k = 0, …, d and n1; …, nd sufficiently large (n ≫ 0)?

(ii) Is the length of the generalized fraction in a polynomial in n for n ≫ 0?

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[1]Auslander, M. and Buchsbaum, D. A.. Codimension and multiplicity. Ann. Math. 68 (1958), 625657.
[2]Cuong, N. T.. On the length of the powers of systems of parameters in local ring. Nagoya Math. J. 120 (1990), 7788.
[3]Cuong, N. T.. On the dimension of the non-Cohen-Macaulay locus of local ring admitting dualizing complexes. Math. Proc. Cambridge Phil. Soc. (2) 109 (1991), 479488.
[4]Cuong, N. T.. On the least degree of polynomials bounding above the differences between lengths and multiplicities of certain systems of parameters in local rings. Nagoya Math. J. 125 (1992), 105114.
[5]Cuong, N. T.. The theory of polynomial types and p-standard ideals in local rings and applications, preprint.
[6]Cuong, N. T., Schenzel, P. and Trung, N. V.. Verallgemeinerte Cohen-Macaulay Moduln. Math. Nach. 85 (1978), 5775.
[7]Garcla Roig, J- I.. On polynomial bounds for the Koszul homology of certain multiplicity systems. J. London Math. Soc. (2) 34 (1986), 411416.
[8]Goto, S. and Yamagishi, K.. The theory of unconditional strong d-sequences and modules of finite local cohomology, preprint.
[9]Kaplansky, I.. Commutative rings (Allyn and Bacon, 1970).
[10]Kirby, D.. Artinian modules and Hilbert polynomials. Quart. J. Math. Oxford (2) 24 (1973), 4757.
[11]MacDonald, I. G.. Secondary representation of modules over a commutative ring. Sympos. Math. 11 (1973), 2343.
[12]Matsumura, H.. Commutative algebra. Second Edition (Benjamin, 1980).
[13]Schenzel, P.. Cohomological annihilators. Math. Proc. Cambridge Phil. Soc. 91 (1982), 345350.
[14]Sharp, R. Y. and Hamieh, M. A.. Lengths of certain generalized fractions. J. Pure Appl. Algebra 38 (1985), 323336.
[15]Sharp, R. Y. and Zakeri, H.. Modules of generalized fractions. Mathematika 29 (1982), 3241.
[16]Sharp, R. Y. and Zakeri, H.. Local cohomology and modules of generalized fractions. Mathematika 29 (1982), 296306.
[17]Sharp, R. Y. and Zakeri, H.. Generalized fractions and the monomial conjecture. J. Algebra 92 (1985), 380388.
[18]Trung, N. V.. Toward a theory of generalized Cohen–Macaulay modules. Nagoya Math. J. 102 (1986), 149.
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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