Pacific Journal of Mathematics

Reductions of filtrations.

J. S. Okon and L. J. Ratliff, Jr.

Article information

Source
Pacific J. Math., Volume 144, Number 1 (1990), 137-154.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102645830

Mathematical Reviews number (MathSciNet)
MR1056670

Zentralblatt MATH identifier
0717.13013

Subjects
Primary: 13A15: Ideals; multiplicative ideal theory
Secondary: 13A30: Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics 13B22: Integral closure of rings and ideals [See also 13A35]; integrally closed rings, related rings (Japanese, etc.)

Citation

Okon, J. S.; Ratliff, L. J. Reductions of filtrations. Pacific J. Math. 144 (1990), no. 1, 137--154. https://projecteuclid.org/euclid.pjm/1102645830


Export citation

References

  • [I] W. Bishop, J. W. Petro, L. J. Ratliff, Jr., and D. E. Rush, Note on Noetherian filtrations, Comm. Algebra, 17 (1989), 471-485.
  • [2] P. Eakin, The converse to a well known theorem on Noetherian rings, Math. Ann., 177(1968), 278-282.
  • [3] J. Lipman and B. Teissier, Pseudo-rational localringsand a theorem ofBriancon- Skoda about integral closuresof ideals, Michigan Math. J., 28 (1981), 97-116.
  • [4] J. Lipman and A. Sathaye, Jacobian ideals and a theorem of Briancon-Skoda, Michigan Math. J., 28 (1981), 199-222.
  • [5] S. McAdam, Asymptotic Prime Divisors, Lecture Notes in Math. No. 1023, Springer-Verlag, New York, 1983.
  • [6] D. G. Northcott and D. Rees, Reductions of ideals in local rings, Math. Proc. Cambridge Philos. Soc, 50 (1954), 145-158.
  • [7] J. S. Okon, Prime divisors,analytic spread and filtrations, Pacific J. Math., 113 (1984), 451-462.
  • [8] J. S. Okon and L. J. Ratliff, Jr., Filtrations, closure operations, and prime divi- sors, Math. Proc. Cambridge Philos. Soc, 104 (1988), 31-46.
  • [9] J. S. Okon and L. J. Ratliff, Filtrations,prime divisors,and Rees rings,Houston J. Math., (to appear).
  • [10] L. J. Ratliff, Jr., A characterization of analytically unramified semi-localrings and applications, Pacific J. Math., 27 (1968), 127-143.
  • [II] L. J. Ratliff, Locally quasi-unmixed Noetherian rings and ideals of the principalclass, Pacific J. Math., 52 (1974), 185-205.
  • [12] L. J. Ratliff, Jr., Notes on essentially powers filiations, Michigan Math. J., 26 (1979), 313-324.
  • [13] L. J. Ratliff, Asymptotic sequences,J. Algebra, 85 (1983), 337-360.
  • [14] L. J. Ratliff, Jr. and D. E. Rush, Note on I-good filiations and Noetherian Rees rings, Comm. Algebra, 16 (1988), 955-975.
  • [15] D. Rees, Asymptotic Propertiesof Ideals, Nagoya Lecture Notes, preprint.
  • [16] D. Rees, Reduction of modules, Math. Proc. Cambridge Philos. So, 101 (1987), 431-449.
  • [17] D. Rees, Semi-Noether filiations: I, J. London Math. Soc, 37 (1988), 43-62.
  • [18] M. Sakuma and H. Okuyama, A criterionfor analytically unramification of a local ring,J. Gakugei, Tokushima Univ., 15 (1966), 36-38.
  • [19] P. Schenzel, Filtrations and Noetherian symbolic blow-up rings, Proc. Amer. Math. Soc, 102 (1988), 817-822.
  • [20] R. Y. Sharp and A.-J. Taherizadeh, Reductions and integral closures of ideals relative to an artinian module, J. London Math. Soc, 37 (1988), 203-218.