Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-30T20:21:53.016Z Has data issue: false hasContentIssue false
  • English
  • Français

A generalization of a theorem of Sharp on big Cohen-Macaulay modules

Published online by Cambridge University Press:  24 October 2008

Santiago Zarzuela
Santiago Zarzuela
Affiliation:
Mathematisches Institut, Universität Köln, Weyertal 86–90, D-5000 Köln 41, Germany
Get access Rights & Permissions [Opens in a new window]

Extract

Let (A, m) be a (commutative, Noetherian) local ring, and a1, …, an a system of parameters for A. Let M be an A-module. We say that M is a big Cohen-Macaulay module with respect to a1, …, an if a1, …, an, is an M-sequence. In this case we call M balanced if any system of parameters for A is an M-sequence.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 108 , Issue 2 , September 1990 , pp. 193 - 195
Copyright
Copyright © Cambridge Philosophical Society 1990

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Bartijn, J. and Strooker, J. R.. Modifications monomiales. In Séminaire d'Algèbre Paul Dubriel et Marie-Paul Malliavin, Paris 1982, Lecture Notes in Math. vol. 1029 (Springer-Verlag, 1983), pp. 192–217.Google Scholar
[2]Bourbaki, N.. Algèbre homologique. Chapitre 10 of Algèbre (Masson, 1980).Google Scholar
[3]Griffith, P.. Maximal Cohen–Macaulay modules and representation theory. J. Pure Appl. Algebra 13 (1978), 321–334.CrossRefGoogle Scholar
[4]Kaplansky, I.. Commutative Rings (The University of Chicago Press, 1974).Google Scholar
[5]Matsumura, H.. Commutative Ring Theory (Cambridge University Press, 1986).Google Scholar
[6]Ogoma, T.. Fibre products of Noetherian rings and their applications. Math. Proc. Cambridge Philos. Soc. 97 (1985), 231–241.CrossRefGoogle Scholar
[7]Sharp, R. Y.. Certain countably generated big Cohen–Macaulay modules are balanced. Math. Proc. Cambridge Philos. Soc. 105 (1989), 73–77.CrossRefGoogle Scholar
[8]Zarzuela, S.. Systems of parameters for non-finitely generated modules and big Cohen–Macaulay modules. Mathematika 35 (1988), 207–215.CrossRefGoogle Scholar