Geodesic
Modularity vs. Separability for Field Extensions
Canadian journal of mathematics, Tome 27 (1975) no. 5, pp. 1176-1182

Voir la notice de l'article provenant de la source Cambridge University Press

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]. 
Kreimer, H. F.; Heerema, N. Modularity vs. Separability for Field Extensions. Canadian journal of mathematics, Tome 27 (1975) no. 5, pp. 1176-1182. doi: 10.4153/CJM-1975-123-2
@article{10_4153_CJM_1975_123_2,
     author = {Kreimer, H. F. and Heerema, N.},
     title = {Modularity vs. {Separability} for {Field} {Extensions}},
     journal = {Canadian journal of mathematics},
     pages = {1176--1182},
     year = {1975},
     volume = {27},
     number = {5},
     doi = {10.4153/CJM-1975-123-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1975-123-2/}
}
TY  - JOUR
AU  - Kreimer, H. F.
AU  - Heerema, N.
TI  - Modularity vs. Separability for Field Extensions
JO  - Canadian journal of mathematics
PY  - 1975
SP  - 1176
EP  - 1182
VL  - 27
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1975-123-2/
DO  - 10.4153/CJM-1975-123-2
ID  - 10_4153_CJM_1975_123_2
ER  - 
%0 Journal Article
%A Kreimer, H. F.
%A Heerema, N.
%T Modularity vs. Separability for Field Extensions
%J Canadian journal of mathematics
%D 1975
%P 1176-1182
%V 27
%N 5
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1975-123-2/
%R 10.4153/CJM-1975-123-2
%F 10_4153_CJM_1975_123_2

[1] 1. Bourbaki, N., Elements de mathématique, Chapter S, Corps commutâtes (Actualités Sci. et Incl., No. 1102, Hermann, Paris, 1950). Google Scholar

[2] 2. Chase, S. U., On inseparable Galois theory, Bull. Amer. Math. Soc. 77 (1971), 413–417. Google Scholar

[3] 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] 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] 5. Gilmer, R. and Heinzer, W., On the existence of exceptional field extensions, Bull. Amer. Math Soc. 74 (1968), 545–547. Google Scholar

[6] 6. Heerema, N., A Galois theory for inseparable field extensions, Trans. Amer. Math. Soc. 154 (1971), 193–200. Google Scholar

[7] 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] 8. Heerema, N. and Tucker, D., Modular field extensions, preprint. Google Scholar

[9] 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] 10. MacLane, S., Modular fields I, Separating transcendence bases, Duke Math. J. ô (1939), 372–393. Google Scholar

[11] 11. Reid, J. D., A note on inseparability, Michigan Math. J. 13 (1966), 219–223. Google Scholar

[12] 12. Sweedler, M. E., Structure of inseparable extensions, Ann. of Math. 87 (1968), 401–410. Google Scholar

Cité par Sources :