Hostname: page-component-6bf8c574d5-w79xw Total loading time: 0 Render date: 2025-02-26T15:20:34.154Z Has data issue: false hasContentIssue false
  • English
  • Français

Fields countably generated over a proper subfield

Published online by Cambridge University Press:  17 April 2009

James K. Deveney  and
Joe Yanik
James K. Deveney
Affiliation:
Department of Mathematical Sciences, Virginia Commonwealth University, Richmond, Virginia 23284., U.S.A.
Joe Yanik
Affiliation:
Department of Mathematical Sciences, Virginia Commonwealth University, Richmond, Virginia 23284., U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

For an arbitrary field K there are two related questions that can be asked:

(1) Is there a proper subfield, L, of K such that K is countably generated over L?

(2) Given a proper subfield M of K is there a proper subfield, L, of K containing M such that K is countably generated over L?

We give an affirmative answer to (1) in characteristic p ≠ 0 and provide counterexamples to (2) for arbitrary characteristic ≠ 2.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 33 , Issue 2 , April 1986 , pp. 219 - 226
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Bialynicki-Birula, A., “On subfields of countable codimension”, Proc. Amer. Math. Soc. 35 (1972), 354–356.CrossRefGoogle Scholar
[2]Jacobson, N., Lectures in abstract algebra, Vol. III. Theory of fields and Galois theory, (Von Nostrand, Princeton, N.J., 1964).Google Scholar