Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-12-02T22:52:03.418Z Has data issue: false hasContentIssue false
  • English
  • Français

Modularity vs. Separability for Field Extensions

Published online by Cambridge University Press:  20 November 2018

H. F. Kreimer  and
N. Heerema
H. F. Kreimer
Affiliation:
Florida State University, Tallahassee, Florida
N. Heerema
Affiliation:
Florida State University, Tallahassee, Florida
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.

In this paper we compare the properties separability and modularity for field extensions. Let be fields of characteristic . K is separable over if K and are linearly disjoint over . K is modular over if K and are linearly disjoint over their intersection for all n > 0. The latter definition is due to Sweedler [12] and is important particularly for Galois theories of purely inseparable extensions [2; 3; 4; 7].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 5 , 01 October 1975 , pp. 1176 - 1182
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Bourbaki, N., Elements de mathématique, Chapter S, Corps commutâtes (Actualités Sci. et Incl., No. 1102, Hermann, Paris, 1950).Google Scholar
2. Chase, S. U., On inseparable Galois theory, Bull. Amer. Math. Soc. 77 (1971), 413–417.Google Scholar
3. Davis, R. L., A Galois theory for a class of purely inseparable field extensions, Dissertation, Florida State University, Tallahassee, Fla., 1969.Google Scholar
4. Gerstenhaber, M. and Zaromp, A., On the Galois theory of purely inseparable field extensions, Bull. Amer. Math. Soc. 76 (1970), 1011–1014.Google Scholar
5. Gilmer, R. and Heinzer, W., On the existence of exceptional field extensions, Bull. Amer. Math Soc. 74 (1968), 545–547.Google Scholar
6. Heerema, N., A Galois theory for inseparable field extensions, Trans. Amer. Math. Soc. 154 (1971), 193–200.Google Scholar
7. Heerema, N. and Deveney, J., Galois theory for fields K/k finitely generated, Trans. Amer. Math. Soc. 189 (1974), 263–274.Google Scholar
8. Heerema, N. and Tucker, D., Modular field extensions, preprint.Google Scholar
9. Jacobson, N., Lectures in abstract algebra III, Theory of fields and Galois theory (D. Van Nostrand Company, Princeton, N.J., 1964).Google Scholar
10. MacLane, S., Modular fields I, Separating transcendence bases, Duke Math. J. ô (1939), 372–393.Google Scholar
11. Reid, J. D., A note on inseparability, Michigan Math. J. 13 (1966), 219–223.Google Scholar
12. Sweedler, M. E., Structure of inseparable extensions, Ann. of Math. 87 (1968), 401–410.Google Scholar