Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-13T08:23:36.158Z Has data issue: false hasContentIssue false
  • English
  • Français

Uniqueness of Subfields

Published online by Cambridge University Press:  20 November 2018

James K. Deveney  and
John N. Mordeson
James K. Deveney
Affiliation:
Virginia Commonwealth University, Richmond, Virginia
John N. Mordeson
Affiliation:
Creighton University, Omaha, Nebraska
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.

Let L be a finitely generated field extension of a field K. The order of inseparability of L/K is the minimum of {n|[L:S] = pn where S is a separable extension of K}. If V is a subfield of L/K, then its order of inseparability is less than or equal to that of L/K. This paper examines the question of when there are unique minimal subfields of order of inseparability n — j, 0 ≤ j ≤ n.

Keywords

12F15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 29 , Issue 2 , 01 June 1986 , pp. 191 - 196
Copyright
Copyright © Canadian Mathematical Society 1986

References

1. Deveney, J. and Mordeson, J., The Order of inseparability of fields, Canad. J. of Math. 31 (1979), pp. 655–662.Google Scholar
2. Deveney, J. and Mordeson, J., Calculating invariants of inseparable field extensions, Proc. Amer. Math. Soc. 81 (1981), pp. 373–376.Google Scholar
3. Deveney, J. and Mordeson, J., Distinguished subfields, T.A.M.S. 260 (1980), pp. 185–193.Google Scholar
4. Deveney, J. and Mordeson, J., Maximal separable subfields of bounded codegree, Proc. Amer. Math. Soc. 88 (1983), pp. 16–20.Google Scholar
5. Gilmer, R. and Heinzer, W., On the existence of exceptional field extensions, Bull. Amer. Math. Soc. 74 (1968), pp. 545–547.Google Scholar
6. Heerema, N., Maximal separable intermediate fields of large codegree, Proc. Amer. Math. Soc. 82 (1981), pp. 351–354.Google Scholar
7. Heerema, N. and Deveney, J., Galois Theory for Fields K/k finitely generated, T.A.M.S. 189 (1974), pp. 263–274.Google Scholar
8. Kraft, H., Inseparable Korpererweiterungen, Comment. Math. Helv. 45 (1970), pp. 110–118.Google Scholar