Let k be a field of arbitrary characteristic. Suppose that f1, . . . , fn are polynomials in k[t] and di = deg(fi). We prove that, if gcd of d1, . . . , dn is 1, then k(f1, . . . , fn) = f(t), or equivalently, the morphism ψ = (f1, . . . , fn) : Ak → A n k is proper and birational onto its image. By combining this result with the epimorphism theorem of… (More)
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