Skip to main content

On equimultiple ideals

This is a preview of subscription content, access via your institution.

References

  • [CN1] Cowsik, R.C., Nori, M.V.: Affine curves in characteristicp are set theoretic complete-intersections, Invent. Math.45, 111–114 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  • [CN2] Cowsik, R.C., Nori, M.V.: On the fibres of blowing up. On the fibres of blowing up. J. Indian Math. Soc.40, 217–222 (1976)

    MATH  MathSciNet  Google Scholar 

  • [GHO] Grothe, U., Herrmann, M., Orbanz, U.: Graded Cohen-Macaulay rings associated to equimultiple ideals. Math. Z.186, 531–556 (1986)

    Article  MathSciNet  Google Scholar 

  • [HI] Herrmann, M., Ikeda, S.: Three notes on the order of ideals defining hypersurfaces. J. Algebra,132, 123–130 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  • [HO1] Herrmann, M., Orbanz, U.: Faserdimension von Aufblasungen lokaler Ringe und Aquimultiplizität. J. Math. Kyoto Univ.20, 651–659 (1980)

    MATH  MathSciNet  Google Scholar 

  • [HO2] Herrmann, M., Orbanz, U.: Normale Flachheit und Aquimultiplizität für vollständige Durchschnitte. J. Algebra70, 437–451 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  • [HO3] Herrmann, M., Orbanz, U.: On equimultiplicity. Math. Proc. Camb. Philos. Soc.91, 207–213 (1982)

    MATH  MathSciNet  Google Scholar 

  • [HO4] Herrmann, M., Orbanz, U.: Between equimultiplicity and normal flatness. In: Aroca, J.M. et al. (eds.) Algebraic geometry. (Lect. Notes Math., vol. 961, pp. 200–232) Berlin Heidelberg New York: Springer 1982

    Chapter  Google Scholar 

  • [HRZ] Herrmann, M., Ribbe, J., Zarzuela, S. (appendix by Ooishi, A.): On Rees and form rings of almost complete intersections. MPI 90-87, Max-Planck-Institut für Mathematik, Bonn

  • [Hi] Hironaka, H.: Resolutions of singularities of an algebraic variety over a field of characteristic 0. Ann. Math.79, 109–326 (1964)

    Article  MathSciNet  Google Scholar 

  • [Ho] Hochster, M.: Criteria for equality of ordinary and symbolic powers of primes. Math. Z.133, 53–65 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  • [Huc] Huckaba, S., Reduction numbers for ideals of higher analytic spread. Math. Proc. Camb. Philos. Soc.102, 49–57 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  • [HM] Huckaba, S., Marley, T.: Depth properties of Rees-algebras and associted graded rings. J. Algebra (to appear)

  • [Hu] Huneke, C.: Hilbert functions and symbolic powers. Mich. Math. J.34, 293–318 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  • [HS] Huneke, C., Sally, J.: Birational extensions in dimension two and integrally closed ideals. J. Algebra115, 481–500 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  • [I1] Itoh, S.: Integral closures of ideals of principal class. Hiroshima Math. J.17, 372–375 (1987)

    MathSciNet  Google Scholar 

  • [I2] Itoh, S.: Integral closures of ideals generated by regular sequences. J. Algebra117, 390–401 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  • [L] Lipman, J.: Equimultiplicity, reduction, and blowing up. (Lect. Notes Pure Appl. Math., vol 68) New York Basel: Dekker 1982

    Google Scholar 

  • [LT] Lipman, J., Teissier, B.: Pseudo-rational local rings and a theorem of Briancon-Skoda about integral closures of ideals. Mich. Math. J.28, 97–116 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  • [M] Matsumura, H.: Commutative Algebra. New York: Benjamin 1970

    MATH  Google Scholar 

  • [NR] Northcott, D., Rees, D.: Reduction of ideals in local rings. Proc. Camb. Philos. Soc.50, 145–158 (1954)

    MATH  MathSciNet  Google Scholar 

  • [O] Ooishi, A.: On the associated graded modules of canonical modules. J. Algebra141, 143–157 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  • [R] Ratliff, J.: Locally quasi-unmixed Noetherian rings and ideals of the principal class. Pac. J. Math.52, 185–205 (1974)

    MATH  MathSciNet  Google Scholar 

  • [Sh1] Shah, K.: On the Cohen-Macaulayness of the fiber cone of an ideal. J. Algebra143, 156–172 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  • [Sh2] Shah, K.: Coefficient ideals. Trans. Am. Math. Soc.327, 373–384 (1991)

    Article  MATH  Google Scholar 

  • [T] Trung, N.: Reduction exponent and degree bound for the defining equations of graded rings. Proc. Am. Math. Soc.101, 229–236 (1987)

    Article  MATH  Google Scholar 

  • [VV] Valabrega, P., Valla, G.: Form rings and regular sequences. Nagoya Math. J.72, 93–101 (1978)

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Shah, K. On equimultiple ideals. Math Z 215, 13–24 (1994). https://doi.org/10.1007/BF02571697

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02571697

Keywords

  • Local Ring
  • Maximal Ideal
  • Short Exact Sequence
  • Noetherian Ring
  • Regular Sequence