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ac.commutative algebra – Product construction of group $mathrm{Aut}(ok(t)[x_1,ldots, x_n])$ Answer

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ac.commutative algebra – Product construction of group $mathrm{Aut}(ok(t)[x_1,ldots, x_n])$

Let $R = ok(t)[x_1,ldots, x_n]$ breathe the polynomial algebra over the bailiwick $ok(t)$ (the place $ok$ is assumed to breathe algebraically closed).

Is it undoubted that $mathrm{Aut}(R) = textual content{ZAut}(R)cdot A_n(R)$?

Where $mathrm{Aut}(R)$ is the automorphism group of $ok(t)$-algebra $R$ and $A_n$ is the subgroup of its affine automorphisms. Also $textual content{ZAut}(R)$ is the clique of $ok(t)$-automorphisms of $R$ such that $alpha (ok[t,x_1,ldots, x_n]) = ok[t,x_1,ldots, x_n]$.

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