Generators of Rings of Constants of Derivations
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چکیده
The aim of this paper is to summarize some motivations and results concerning generators of rings of constants of derivations, especially in the positive characteristic case. 1. Preliminaries. Let k be a field of characteristic p > 0. Denote by k[X] the polynomial algebra k[x1, . . . , xn] and by k(X) the field of rational functions k(x1, . . . , xn). A k-linear mapping d : k[X] → k[X] is called a k-derivation of k[X] if d(fg) = fd(g) + gd(f) for all f, g ∈ k[X]. For any g1, . . . , gn ∈ k[X] there exists the unique kderivation d of k[X] such that d(x1) = g1, . . . , d(xn) = gn. This derivation is of the form
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