The Picard–vessiot Antiderivative Closure
نویسندگان
چکیده
F is a differential field of characteristic zero with algebraically closed field of constants C. A Picard–Vessiot antiderivative closure of F is a differential field extension E ⊃ F which is a union of Picard–Vessiot extensions of F , each obtained by iterated adjunction of antiderivatives, and such that every such Picard– Vessiot extension of F has an isomorphic copy in E. The group G of differential automorphisms of E over F is shown to be prounipotent. When C is the complex numbers and F = C(t) the rational functions in one variable, G is shown to be free
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