A Galois theory for a class of inseparable field extensions

Davis, R. L.

doi:10.1090/S0002-9947-1975-0379453-3

A Galois theory for a class of inseparable field extensions
HTML articles powered by AMS MathViewer

by R. L. Davis PDF

Trans. Amer. Math. Soc. 213 (1975), 195-203 Request permission

Abstract:

The structure of the group of rank n higher derivations in a field K is discussed and a characterization of its Galois subgroups is given. This yields a Galois type correspondence between these subgroups and the subfields over which K is purely inseparable, finite dimensional and modular.

References

R. L. Davis, A Galois theory for a class of purely inseparable exponent two field extensions, Bull. Amer. Math. Soc. 75 (1969), 1001–1004. MR 244207, DOI 10.1090/S0002-9904-1969-12334-7
Murray Gerstenhaber, On the Galois theory of inseparable extensions, Bull. Amer. Math. Soc. 70 (1964), 561–566. MR 162794, DOI 10.1090/S0002-9904-1964-11201-5
Murray Gerstenhaber, On infinite inseparable extensions of exponent one, Bull. Amer. Math. Soc. 71 (1965), 878–881. MR 188206, DOI 10.1090/S0002-9904-1965-11424-0
Nickolas Heerema, Convergent higher derivations on local rings, Trans. Amer. Math. Soc. 132 (1968), 31–44. MR 223358, DOI 10.1090/S0002-9947-1968-0223358-1
Nickolas Heerema, Derivations and embeddings of a field in its power series ring. II, Michigan Math. J. 8 (1961), 129–134. MR 136601
Nickolas Heerema, A Galois theory for inseparable field extensions, Trans. Amer. Math. Soc. 154 (1971), 193–200. MR 269632, DOI 10.1090/S0002-9947-1971-0269632-4
N. Jacobson, Galois theory of purely inseparable fields of exponent one, Amer. J. Math. 66 (1944), 645–648. MR 11079, DOI 10.2307/2371772
Nathan Jacobson, Lectures in abstract algebra. Vol III: Theory of fields and Galois theory, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London-New York, 1964. MR 0172871, DOI 10.1007/978-1-4612-9872-4
Nathan Jacobson, Lie algebras, Interscience Tracts in Pure and Applied Mathematics, No. 10, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0143793
M. Ojanguren and R. Sridharan, A note on purely inseparable extensions, Comment. Math. Helv. 44 (1969), 457–461. MR 257054, DOI 10.1007/BF02564544
Moss Eisenberg Sweedler, Structure of inseparable extensions, Ann. of Math. (2) 87 (1968), 401–410. MR 223343, DOI 10.2307/1970711
Morris Weisfeld, Purely inseparable extensions and higher derivations, Trans. Amer. Math. Soc. 116 (1965), 435–449. MR 191895, DOI 10.1090/S0002-9947-1965-0191895-1