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Higher Derivations and Tensor Products of Commutative Rings
Published online by Cambridge University Press: 20 November 2018
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The genesis of this paper is the following well known result in field theory: Let R denote a field of characteristic p ≠ 0, and let 
denote a subfield of R such that 
for some e sufficiently large. Then R is isomorphic to the tensor product (over 
) of primitive extensions of 
if and only if there exists a finite set Γ of 
-higher derivations on R such that 
is the field of constants of Γ. A proof of this theorem can be found in [6].
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- Research Article
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- Copyright © Canadian Mathematical Society 1978
References
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Heerema, N., Higher derivations and automorphisms of complete local rings, Bull. Amer. Math. Soc. 76 (1970), 1212–1225.Google Scholar
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Jacobson, N., Lectures in abstract algebra, III (D. Van Nostrand Co., Princeton, New Jersey).Google Scholar
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Ribenboim, P., Higher derivations of rings I, Rev. Roum. Math Pures et Appl. 16 (1971), 77–110.Google Scholar
6.
Weisfeld, M., Purely inseparable extensions and higher derivations, Trans-Amer. Math. Soc. 116 (1965), 435–450.Google Scholar
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