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Higher Derivations and Tensor Products of Commutative Rings

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].