Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-26T17:40:00.610Z Has data issue: false hasContentIssue false
  • English
  • Français

Pure Subfields of Purely Inseparable Field Extensions

Published online by Cambridge University Press:  20 November 2018

James K. Deveney
James K. Deveney*
Affiliation:
Virginia Commonwealth University, Richmond, Virginia
Rights & Permissions [Opens in a new window]

Extract

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.

The notion of pure subgroups is due to Prufer [7]. It has proven extremely useful in establishing structural properties of abelian groups. In a recent paper [9], Waterhouse introduced the concept of a pure subfield of a purely inseparable extension. Let L be a purely inseparable modular extension of k, and let K be an intermediate field. K is called pure if K and k(Lpn) are linearly disjoint over k(Kpn) for all n. Waterhouse used this concept to establish the existence of basic subfields [9].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 6 , 01 December 1976 , pp. 1162 - 1166
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Heerema, N. and Deveney, J., Galois theory for fields K/k finitely generated, Trans. Amer. Math. Soc. 189 (1974), 263–274.Google Scholar
2. Deveney, J., An intermediate theory for a purely inseparable Galois theory, Trans. Amer. Math. Soc. 198 (1974), 287–295.Google Scholar
3. Kime, L. A., Purely inseparable modular extensions of unbounded exponent, Trans. Amer. Math. Soc. 176 (1973), 335–349.Google Scholar
4. Jacobson, N., Lectures in abstract algebra. Vol. Ill: Theory of fields and Galois theory (Van Nostrand, Princeton, New Jersey, 1964).Google Scholar
5. Mordeson, J. and Vinograde, B., Structure of arbitrary purely inseparable extensions fields, Lecture Notes in Math., Vol. 173 (Springer-Verlag, Berlin and New York, 1970).Google Scholar
6. Mordeson, J. and Vinograde, B., Generators and tensor factors of purely inseparable fields, Math. Z. 107 (1968), 326–334.Google Scholar
7. Prufer, H., Untersuchungen uber die Zerlegbarkeit der abzahlbaren primaren abelschen Gruppen, Math. Z. 17 (1923), 35–61.Google Scholar
8. Sweedler, M. E., Structure of inseparable extensions, Ann. of Math. (2) 87 (1968), 401–410.Google Scholar
9. Waterhouse, W. C., The structure of inseparable field extensions, Trans. Amer. Math. Soc. 211 (1975), 39–56.Google Scholar