Skip to main content
Log in

An implicit function theorem for algebraically closed fields

  • Published:
Algebra universalis Aims and scope Submit manuscript

Abstract

Let F be an algebraically closed field of characteristic 0, and let f : F nF. We show that f is implicitly definable by a system of polynomial equations if and only if f is a special kind of piecewise rational function.

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.

Institutional subscriptions

Similar content being viewed by others

References

  1. Burris S., Sankappanavar H.P.: A Course in Universal Algebra. Springer, New York (1981)

    MATH  Google Scholar 

  2. Campercholi M., Vaggione D.: An implicit function theorem for regular fuzzy logic functions. Fuzzy Sets and Systems 159, 2983–2987 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  3. Campercholi, M., Vaggione, D.: Algebraic functions (2009, preprint)

  4. Campercholi M., Vaggione D.: Algebraically expandable classes. Algebra Universalis 61, 151–186 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  5. Volger H.: Preservation theorems for limits of structures and global sections of sheaves of structures. Math. Z. 166, 27–54 (1979)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Miguel A. Campercholi.

Additional information

Presented by K. Kaarli.

The research of both authors was supported by a grant from SECYT-UNC.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Campercholi, M.A., Vaggione, D.J. An implicit function theorem for algebraically closed fields. Algebra Univers. 65, 299–304 (2011). https://doi.org/10.1007/s00012-011-0130-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00012-011-0130-7

2010 Mathematics Subject Classification

Key words and phrases

Navigation