Advertisement

Constructing the Completion of a Field Using Quasimorphisms

  • 14 Accesses

Abstract

We explain how the construction of the real numbers using quasimorphisms can be transformed into a general method to construct the completion of a field with respect to an absolute value.

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

Access options

Buy single article

Instant unlimited access to the full article PDF.

US$ 39.95

Price includes VAT for USA

References

  1. 1.

    N. A’Campo, “A natrural construction for the real numbers,” arxiv:math/0301015, (2003).

  2. 2.

    R. D. Arthan, “The Eudoxus real numbers,” arXiv:math/0405454, (2004).

  3. 3.

    E. Bloch, The Real Numbers and Real Analysis (Springer, New York, 2011).

  4. 4.

    T. Grundhöfer, “Describing the real numbers in terms of integers,” Arch. Math. (Basel) 85, 79–81 (2005).

  5. 5.

    J. Neukirch, Algebraic Number Theory (Springer, Berlin, 1999).

  6. 6.

    G. Pilz, Near-Rings (North-Holland Publishing Company, Amsterdam, 1977).

  7. 7.

    R. Street, “An efficient construction of real numbers,” Austral. Math. Soc. Gaz. 12, 57–58 (1985).

  8. 8.

    I. Weiss, “Survey article: The real numbers–a survey of constructions,” Rocky Mountain J. Math. 45, 737–

Download references

Acknowledgements

We thank an anonymous referee for pointing us to the notion of near-rings.

Funding

The research was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - 338540207.

Author information

Correspondence to Steffen Kionke.

Additional information

The text was submitted by the author in English.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Kionke, S. Constructing the Completion of a Field Using Quasimorphisms. P-Adic Num Ultrametr Anal Appl 11, 335–337 (2019). https://doi.org/10.1134/S2070046619040083

Download citation

Key words

  • completion
  • quasimorphisms
  • near-rings