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Systems of parameters for non-finitely generated modules and big Cohen–Macaulay modules

Part of: Chain conditions, finiteness conditions

Published online by Cambridge University Press:  26 February 2010

Santiago Zarzuela
Santiago Zarzuela
Affiliation:
Departament d'Algebra i Geometria, Facultat de Matematiques, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain.
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Extract

Let (R, ) be a commutative Noetherian local ring. We investigate conditions for a non-finitely generated R-module M to have a system of parameters. We prove that if

then any system of parameters for R/AnR (M) is a system of parameters for M. As an application we characterize by means of systems of parameters those balanced big Cohen–Macaulay R-modules M for which SuppR (M) = suppR (M).

MSC classification

Secondary: 13E05: Noetherian rings and modules
Type
Research Article
Information
Mathematika , Volume 35 , Issue 2 , December 1988 , pp. 207 - 215
Copyright
Copyright © University College London 1988

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References

1.Bartjin, J. and Strooker, J. R.. Modifications monomiales, in: Séminaire d'Algèbre Dubreil-Malliavin, Paris 1982, Lecture Notes in Math. 1029 (Springer, 1982).Google Scholar
2.Foxby, H.-B.. On the μi n a minimal injective resolution II. Math. Scand., 41 (1977), 19–44.CrossRefGoogle Scholar
3.Foxby, H.-B.. Bounded complexes of flat modules. J. Pure Appl. Algebra, 15 (1979), 149–172.CrossRefGoogle Scholar
4.Griffith, P.. A representation theorem for complete local rings. J. Pure Appl. Algebra, 7 (1976), 303–315.CrossRefGoogle Scholar
5.Hergoz, J. and Kunz, E.. Der Kanonische modul eines Cohen-Macaulay-Rings. Lecture Notes in Math., 238 (Springer, 1971).Google Scholar
6.Hochster, M.. Topics in the homological theory of modules over commutative rings. CBMS Regional Conference series in Mathematics, 24 (A.M.S., 1974).Google Scholar
7.Matsumura, H.. Commutative Algebra (Benjamin/Cummings, 1980).Google Scholar
8.Ratliff, L. J. Jr. Catenary rings and the altitude formula. Amer. J. Math., 94 (1972), 458–466.CrossRefGoogle Scholar
9.Sharp, R. Y.. Cohen-Macaulay properties for balanced big Cohen-Macaulay modules. Math. Proc. Camb. Phil. Soc., 90 (1981), 229–238.CrossRefGoogle Scholar
10.Sharp, R. Y.. A Cousin complex characterization of balanced big Cohen-Macaulay modules. Quart. J. Math. Oxford (2), 33 (1982), 471–485.CrossRefGoogle Scholar
11.Sharp, R. Y.. Local cohomology and the Cousin complex for a commutative Noetherian ring. Math. Z., 153 (1977), 19–22.CrossRefGoogle Scholar
12.Sharp, R. Y.. Gorenstein modules. Math. Z., 115 (1970), 117–139.CrossRefGoogle Scholar
13.Sharpe, D. W. and Vamos, P.. Injective modules (Cambridge University Press, 1972).Google Scholar
14.Takeuchi, Y. and Hiromori, K.. On F-modules and balanced big Cohen-Macaulay modules. Math. Seminar Notes, Kobe University, 10 (1982), 595–608.Google Scholar
15.Zarzuela, S.. Balanced big Cohen–Macaulay modules and flat extensions of rings. Math. Proc. Camb. Phil. Soc., 102 (1987), 203–209.CrossRefGoogle Scholar