Skip to main content
Log in

On the heights of prime ideals under integral extensions

  • Published:
Archiv der Mathematik Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. I. S. Cohen andA. Seidenberg, Prime ideals and integral dependence. Bull. Amer. Math. Soc.52, 252–261 (1946).

    Article  MathSciNet  Google Scholar 

  2. R.Gilmer, Multiplicative Ideal Theory. Kingston, Ontario, Canada 1968.

  3. R.Gilmer, Multiplicative Ideal Theory. New York 1972.

  4. W. Heinzer, Integral ring extensions and prime ideals of infinite rank. Proc. Amer. Math. Soc.28, 344–346 (1971).

    Article  MathSciNet  Google Scholar 

  5. I.Kaplansky, Commutative Rings. Boston 1970.

  6. W. Krull, Jacobsonsche Ringe, Hilbertsche Nullstellensatz, Dimensionstheorie. Math. Z.54, 354–387 (1951).

    Article  MathSciNet  Google Scholar 

  7. E.Kunz, Introduction to Commutative Algebra and Algebraic Geometry. Boston 1985.

    Chapter  Google Scholar 

  8. M.Nagata, Local Rings. New York 1962.

Download references

Author information

Authors and Affiliations

Authors

Additional information

This author received partial support from National Science Foundation Grant DMS-8501003.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gilmer, R., Nashier, B. & Nichols, W. On the heights of prime ideals under integral extensions. Arch. Math 52, 47–52 (1989). https://doi.org/10.1007/BF01197970

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01197970

Keywords

Navigation