Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-24T05:21:47.402Z Has data issue: false hasContentIssue false

Subfields and Invariants of Inseparable Field Extensions

Published online by Cambridge University Press:  20 November 2018

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

Let L/K be a field extension of characteristic p ≠ 0. The existence of intermediate fields over which L is regular, separable, or modular is important in recent Galois theories. For instance, see [1; 2; 3; 4; 7; 8; 9 and 14].

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Chase, S., On inseparable Galois theory, Bull. Amer. Math. Soc. 77 (1971), 413417,Google Scholar
2. Davis, R., Higher derivations and field extensions, Trans. Amer. Math. Soc. 180 (1973), 4752.Google Scholar
3. Deveney, J., Fields of constants of infinite higher derivations, Proc. Amer. Math. Soc. 41 (1973), 394398.Google Scholar
4. Deveney, J. An intermediate theory for a purely inseparable Galois theory, Trans. Amer. Math. Soc. 198 (1974), 287295.Google Scholar
5. Deveney, J. A counterexample concerning inseparable field extensions, Proc. Amer. Math. Soc. 55 (1976), 3334.Google Scholar
6. Dieudonne, J., Sur les extensions transcendantes separables, Summa Brasil Math. 2 (1947), 120.Google Scholar
7. Gerstenhaber, M. and Zaromp, A., On the Galois theory of purely inseparable field extensions, Bull. Amer. Math. Soc. 76 (1970), 10111014.Google Scholar
8. Heerema, N., A galois theory for inseparable field extensions, Trans. Amer. Math. Soc. 154 (1971), 193200.Google Scholar
9. Heerema, N. and Deveney, J., Galois theory for fields K/k finitely generated, Trans. Amer. Math. Soc. 189 (1974), 263274.Google Scholar
10. Heerema, N. and Tucker, D., Modular field extensions, Proc. Amer. Math. Soc. 53 (1975), 16.Google Scholar
11. Kime, L., Purely inseparable, modular extensions of unbounded exponent, Trans. Amer. Math. Soc. 176 (1973), 335349.Google Scholar
12. Kraft, H., Inseparable Korpererweiterungen, Comment. Math. Helv. 45 (1970), 110118.Google Scholar
13. Kreimer, H. and Heerema, N., Modularity vs. separability for field extensions, Can. J. Math. 27 (1975), 11761182.Google Scholar
14. Mordeson, J., On a Galois theory for inseparable field extensions, Trans. Amer. Math. Soc. (1975), 337347.Google Scholar
15. Mordeson, J. Splitting of field extensions, Archiv der Mathematik 26 (1975), 606610.Google Scholar
16. Mordeson, J. and Vinograde, B., Structure of arbitrary purely inseparable extension fields, Lecture Notes in Math., Vol. 173 (Springer-Verlag, New York, 1970).Google Scholar
17. Mordeson, J. and Vinograde, B. Separating p-basis and transcendental extension fields, Proc. Amer. Math. Soc. 31, (1972), 417422.Google Scholar
18. Mordeson, J. and Vinograde, B. Relatively separated transcendental field extensions, Archiv der Mathematik 24 (1973), 521526.Google Scholar
19. Mordeson, J. and Vinograde, B. Inseparable embeddings of separable transcendental extensions, Archiv der Mathematik 27 (1976), 4247.Google Scholar
20. Pickert, G., Inseparable Korpererweiterungen, Math. Zeit. 52 (1949), 81135.Google Scholar
21. Waterhouse, W., The structure of inseparable field extensions, Trans. Amer. Math. Soc. 211 (1975), 3956.Google Scholar