Derivation of prime rings of positive characteristic

Let L be a finite-dimensional differential Lie algebra acting on a prime ring R and let the inner part {ie49-1} of L be quasi-Frobenius. Then a constant ring R^L is prime iff {ie49-2} is a differentially simple ring. A ring of constants is semiprime iff {ie49-3} is a direct sum of differentially simple rings, and the prime dimension of a constant ring is equal to the number of differentially simple summands {ie49-4}. The Galois closure of L is obtained from L by adding all the inner derivations of a symmetric Martindale quotient ring which agree with elements from {ie49-5}. Supported by RFFR grant No. 93-01-16171 and by ISF grant RPS000-RPS300. Translated fromAlgebra i Logika, Vol. 35, No. 1, pp. 88–104, January–February, 1996.