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Higher Derivations and Tensor Products of Commutative Rings

Published online by Cambridge University Press:  20 November 2018

W. C. Brown
W. C. Brown*
Affiliation:
Michigan Skite University, East Lansing, Michigan
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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].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 2 , 01 April 1978 , pp. 401 - 418
Copyright
Copyright © Canadian Mathematical Society 1978

References

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3. Jacobson, N., Lectures in abstract algebra, III (D. Van Nostrand Co., Princeton, New Jersey).Google Scholar
4. Nakai, V., High order derivations I, Osaka J. Math. 7 (1970), 1–27.Google Scholar
5. 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