# polynomials – Product construction of group \$Aut(okay(t)[x_1,ldots, x_n])\$ Answer

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polynomials – Product construction of group \$Aut(okay(t)[x_1,ldots, x_n])\$

$$R = okay(t)[x_1,ldots, x_n]$$– polynomial algebra over bailiwick $$okay(t)$$ ($$okay$$ is assumed to breathe closed)

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

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

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