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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
DOI: https://doi.org/10.1090/S0002-9947-1974-0335482-6
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.


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DOI: https://doi.org/10.1090/S0002-9947-1974-0335482-6
Keywords: Differential algebra, Kähler differentials, differential ring, differential module, Ritt basis theorem, nonzero characteristic
Article copyright: © Copyright 1974 American Mathematical Society