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edited Apr 13, 2017 at 12:58

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A prolongation of the question composition-of-polynomial-functions-which-gives-the-identity composition-of-polynomial-functions-which-gives-the-identity: Let $f_1,\ldots,f_n, g_1,\ldots, g_n$ be polynomials in $\mathbb{Q}[X_1,\ldots,X_n]$ such that if $g=(g_1,\ldots,g_n)$ then $f_i(g(x_1,\ldots,x_n))=x_i$ for all $i=1,\ldots,n$. Does it follow that SOME $f_i$ or $g_j$ has degree 1?

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edited Dec 18, 2011 at 15:14

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polinomials polynomials

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asked Dec 18, 2011 at 15:10

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polynomial maps

A prolongation of the question composition-of-polynomial-functions-which-gives-the-identity: Let $f_1,\ldots,f_n, g_1,\ldots, g_n$ be polynomials in $\mathbb{Q}[X_1,\ldots,X_n]$ such that if $g=(g_1,\ldots,g_n)$ then $f_i(g(x_1,\ldots,x_n))=x_i$ for all $i=1,\ldots,n$. Does it follow that SOME $f_i$ or $g_j$ has degree 1?

polinomials