Skip to main content

On the number of generators of ideals of dimension zero

  • 3033 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 311)

Abstract

This note contains generalizations of two results of Abhyankar [1] which give a bound for the embedding dimension of certain local rings in terms of the multiplicity and the dimension of the ring.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   54.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   69.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abhyankar, S. S., "Local rings of high embedding dimension", Amer. J. Math. 89 (1967), 1073–1077.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. Abhyankar, S. S., Resolutions of Singularities of Embedded Algebraic Surfaces, Academic Press, New York, 1966.

    MATH  Google Scholar 

  3. Nagata, M., Local Rings, Interscience, New York, 1962.

    MATH  Google Scholar 

  4. Swan, R. G., "The number of generators of a module", Math. Zeit. 102 (1967), 318–322.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. Zariski, O. and Samuel, P., Commutative Algebra, vol. II, D. Van Nostrand, New York, 1960

    CrossRef  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1973 Springer-Verlag

About this paper

Cite this paper

Sally, J. (1973). On the number of generators of ideals of dimension zero. In: Brewer, J.W., Rutter, E.A. (eds) Conference on Commutative Algebra. Lecture Notes in Mathematics, vol 311. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0068932

Download citation

  • DOI: https://doi.org/10.1007/BFb0068932

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06140-3

  • Online ISBN: 978-3-540-38340-6

  • eBook Packages: Springer Book Archive