Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-26T11:24:50.261Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical criteria for integral dependence

Published online by Cambridge University Press:  27 April 2011

BERND ULRICH  and
JAVID VALIDASHTI
BERND ULRICH
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, IN 47907, U.S.A. e-mail: [email protected]
JAVID VALIDASHTI
Affiliation:
Department of Mathematics, University of Kansas, Lawrence, KS 66045, U.S.A. e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We study multiplicity based criteria for integral dependence of modules or of standard graded algebras, known as ‘Rees criteria’. Rather than using the known numerical invariants, we achieve this goal with a more direct approach by introducing a multiplicity defined as a limit superior of a sequence of normalized lengths; this multiplicity is a non-negative real number that can be irrational.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 151 , Issue 1 , July 2011 , pp. 95 - 102
Copyright
Copyright © Cambridge Philosophical Society 2011

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]Achilles, R. and Manaresi, M.Multiplicity for ideals of maximal analytic spread and intersection theory. J. Math. Kyoto Univ. 33 (1993), 1029–1046.Google Scholar
[2]Buchsbaum, D. A. and Rim, D. S.A generalized Koszul complex, II. Depth and multiplicity. Trans. Amer. Math. Soc. 111 (1964), 197–224.CrossRefGoogle Scholar
[3]Cutkosky, S. D.. Hà, H. T., Srinivasan, H. and Theodorescu, E.Asymptotic behavior of the length of local cohomology. Canad. J. Math. 57 (2005), 1178–1192.CrossRefGoogle Scholar
[4]Cutkosky, S. D., Herzog, J. and Srinivasan, H.Asymptotic growth of algebras associated to powers of ideals. Math. Proc. Camb. Phil. Soc. 148 (2010), 55–72.CrossRefGoogle Scholar
[5]Herzog, J., Puthenpurakal, T. J. and Verma, J. K.Hilbert polynomials and powers of ideals. Math. Proc. Camb. Phil. Soc. 145 (2008), 623–642.CrossRefGoogle Scholar
[6]Matsumura, H.Commutative Ring Theory. (Cambridge University Press, 1989).Google Scholar
[7]Simis, A., Ulrich, B. and Vasconcelos, W. V.Codimension, multiplicity and integral extensions. Math. Proc. Camb. Phil. Soc. 130 (2001), 237–257.CrossRefGoogle Scholar
[8]Simis, A. and Vasconcelos, W. V.Krull dimension and integrality of symmetric algebras. Manuscripta Math. 61 (1988), 63–78.CrossRefGoogle Scholar
[9]Ulrich, B. and Validashti, J.A criterion for integral dependence of modules. Math. Res. Lett. 15 (2008), 149–162.CrossRefGoogle Scholar
[10]Validashti, J.Relative multiplicities of graded algebras. J. Algebra 333 (2011), 14–25.CrossRefGoogle Scholar