Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-25T13:40:23.846Z Has data issue: false hasContentIssue false
  • English
  • Français

Differential fields and differentiable functions of algebraic numbers

Published online by Cambridge University Press:  24 October 2008

Eric F. Müller
Eric F. Müller
Affiliation:
Max-Planck-Straβe 1, 81627 München, Germany
Get access Rights & Permissions [Opens in a new window]

Abstract

We prove that each countable differential field of characteristic 0 can be embedded into the differential ring of infinitely differentiable functions from the algebraic numbers to the complex numbers. This statement remains valid when we replace the set of algebraic numbers by an arbitrary non-empty countable set of complex numbers without any isolated points.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 118 , Issue 2 , September 1995 , pp. 341 - 350
Copyright
Copyright © Cambridge Philosophical Society 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Körner, T. W.. Differentiable functions on the rationale. Bull. London Math. Soc. 23 (1991) 557–562.CrossRefGoogle Scholar
[2]Van der Waerden, B. L.. Algebra I (Springer, 1971).CrossRefGoogle Scholar