Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-26T08:46:20.587Z Has data issue: false hasContentIssue false
  • English
  • Français

On asymptotic stability for sets of prime ideals connected with the powers of an ideal

Published online by Cambridge University Press:  24 October 2008

Leif Melkersson
Leif Melkersson
Affiliation:
Department of Mathematics, University of Lund, Box 118, S-221 00 Lund, Sweden
Get access Rights & Permissions [Opens in a new window]

Extract

The notion of associated prime ideal and the related one of primary decomposition are classical. In a dual way one defines attached prime ideals and secondary representation. This theory is developed in the appendix to §6 in Matsumura[5] and in Macdonald[3].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 107 , Issue 2 , March 1990 , pp. 267 - 271
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]Brodmann, M.. Asymptotic stability of Ass(M/InM). Proc. Amer. Math. Soc. 74 (1979), 16–18.Google Scholar
[2]Kirby, T.. Artinian modules and Hilbert polynomials. Quart. J. Math. Oxford Ser. (2) 24 (1973), 47–57.CrossRefGoogle Scholar
[3]Macdonald, I. G.. Secondary representations of modules over a commutative ring. In Symposia Mathematica 11 (Academic Press, 1973), pp. 23–43.Google Scholar
[4]Matsumura, H.. Commutative algebra, 2nd ed. (Benjamin/Cummings, 1980).Google Scholar
[5]Matsumura, H.. Commutative ring theory (Cambridge University Press, 1986).Google Scholar
[6]McAdam, S.. Asymptotic prime divisors. Lecture Notes in Math. vol. 1023 (Springer-Verlag, 1983).CrossRefGoogle Scholar
[7]Ratliff, L. J.. On asymptotic prime divisors. Pacific J. Math. 111 (1984), 395–413.CrossRefGoogle Scholar
[8]Sharp, R. Y.. Asymptotic behaviour of certain sets of attached prime ideals. J. London Math. Soc. (2) 34 (1986), 212–218.CrossRefGoogle Scholar
[9]Sharp, R. Y. and Taherizadeh, A.-J.. Reductions and integral closures of ideals relative to an artinian module. J. London Math. Soc. (2) 37 (1988), 203–218.CrossRefGoogle Scholar