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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Kähler differentials and differential algebra in arbitrary characteristic

Author: Joseph Johnson
Journal: Trans. Amer. Math. Soc. 192 (1974), 201-208
MSC: Primary 12H05
MathSciNet review: 0335482
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Abstract: Let L and K be differential fields with L an extension of K. It is shown how the module of Kähler differentials $ \Omega _{L/K}^1$ can be used to ``linearize'' properties of a differential field extension $ L/K$. This is done without restriction on the characteristic p and yields a theory which for $ p \ne 0$ is no harder than the case $ p = 0$. As an application a new proof of the Ritt basis theorem is given.

References [Enhancements On Off] (What's this?)

  • [1] Solomon Lefschetz, Algebraic geometry, Princeton Univ. Press, Princeton, N.J., 1953, Chap 3, §3. MR 15, 150. MR 0056950 (15:150h)
  • [2] Joseph Johnson, A notion of Krull dimension for differential rings, Comment. Math. Helv. 44 (1969), 207-216. MR 39 #4127. MR 0242800 (39:4127)
  • [3] -, Kähler differentials and differential algebra, Ann. of Math. (2) 89 (1969), 92-98. MR 39 #187. MR 0238823 (39:187)
  • [4] Abraham Seidenberg, Some basic theorems in partial differential algebra, Mem. Coll. Sci. Univ. Kyoto Ser. A Math. 31 (1958), 1-8. MR 20 #4099. MR 0097631 (20:4099)
  • [5] A. Grothendieck and J. Dieudonné, Éléments de géométrie algébrique. IV. Étude locale des schémas et des morphismes de schémas. I, Inst. Hautes Études Sci. Publ. Math. No. 20 (1964), 259 pp. MR 30 #3885. MR 0173675 (30:3885)
  • [6] E. R. Kolchin, Differential algebra and algebraic groups, Academic Press, New York, 1973. MR 0568864 (58:27929)

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Keywords: Differential algebra, Kähler differentials, differential ring, differential module, Ritt basis theorem, nonzero characteristic
Article copyright: © Copyright 1974 American Mathematical Society

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