Hostname: page-component-848d4c4894-2pzkn Total loading time: 0 Render date: 2024-06-08T21:22:38.195Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

1. Bourbaki, N., Algèbre commutative (Hermann, Paris).Google Scholar
2. Heerema, N., Higher derivations and automorphisms of complete local rings, Bull. Amer. Math. Soc. 76 (1970), 1212–1225.Google Scholar
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