Central separable algebras with purely inseparable splitting rings of exponent one

Yuan, Shuen

doi:10.1090/S0002-9947-1971-0268175-1

Central separable algebras with purely inseparable splitting rings of exponent one

Author: Shuen Yuan
Journal: Trans. Amer. Math. Soc. 153 (1971), 427-450
MSC: Primary 13.80
DOI: https://doi.org/10.1090/S0002-9947-1971-0268175-1
MathSciNet review: 0268175
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Classical Galois cohomological results for purely inseparable field extensions of exponent one are generalized here to commutative rings of prime characteristic.

[1] S. A. Amitsur, Simple algebras and cohomology groups of arbitrary fields, Trans. Amer. Math. Soc. 90 (1959), 73–112. MR 101265, https://doi.org/10.1090/S0002-9947-1959-0101265-7
[2] Maurice Auslander and Oscar Goldman, The Brauer group of a commutative ring, Trans. Amer. Math. Soc. 97 (1960), 367–409. MR 121392, https://doi.org/10.1090/S0002-9947-1960-0121392-6
[3] Hyman Bass, Algebraic 𝐾-theory, W. A. Benjamin, Inc., New York-Amsterdam, 1968. MR 0249491
[4] Astrid J. Berkson, On Amitsur’s complex and restricted Lie algebras, Trans. Amer. Math. Soc. 109 (1963), 430–443. MR 158916, https://doi.org/10.1090/S0002-9947-1963-0158916-1
[5] N. Bourbaki, Algèbre commutative. Chaps. 1, 2, Actualités Sci. Indust., no. 1290, Hermann, Paris, 1961. MR 36 #146.
[6] Henri Cartan and Samuel Eilenberg, Homological algebra, Princeton University Press, Princeton, N. J., 1956. MR 0077480
[7] Pierre Cartier, Questions de rationalité des diviseurs en géométrie algébrique, Bull. Soc. Math. France 86 (1958), 177–251 (French). MR 106223
[8] S. U. Chase and Alex Rosenberg, Amitsur cohomology and the Brauer group, Mem. Amer. Math. Soc. No. 52 (1965), 34–79. MR 0195923
[9] A. Grothendieck and J. Dieudonné, Éléments de géométrie algébrique. I, Inst. Hautes Études Sci. Publ. Math. No. 4 (1960). MR 36 #177a.
[10] G. Hochschild, Restricted Lie algebras and simple associative algebras of characteristic 𝑝, Trans. Amer. Math. Soc. 80 (1955), 135–147. MR 72428, https://doi.org/10.1090/S0002-9947-1955-0072428-0
[11] G. Hochschild, Simple algebras with purely inseparable splitting fields of exponent 1, Trans. Amer. Math. Soc. 79 (1955), 477–489. MR 70961, https://doi.org/10.1090/S0002-9947-1955-0070961-9
[12] Alex Rosenberg and Daniel Zelinsky, On Amitsur’s complex, Trans. Amer. Math. Soc. 97 (1960), 327–356. MR 121391, https://doi.org/10.1090/S0002-9947-1960-0121391-4
[13] Alex Rosenberg and Daniel Zelinsky, Amitsur’s complex for inseparable fields, Osaka Math. J. 14 (1962), 219–240. MR 142604
[14] Shuen Yuan, On the theory of 𝑝-algebras and the Amitsur cohomology groups for inseparable field extensions, J. Algebra 5 (1967), 280–304. MR 228548, https://doi.org/10.1016/0021-8693(67)90041-5
[15] Shuen Yuan, On logarithmic derivatives, Bull. Soc. Math. France 96 (1968), 41–52. MR 237482
[16] Shuen Yuan, Inseparable Galois theory of exponent one, Trans. Amer. Math. Soc. 149 (1970), 163–170. MR 257063, https://doi.org/10.1090/S0002-9947-1970-0257063-1
[17] Shuen Yuan, On the Brauer groups of local fields, Ann. of Math. (2) 82 (1965), 434–444. MR 184978, https://doi.org/10.2307/1970706