2 problems

Let $k$ be a field of characteristic $0$, and let $f$ and $g$ be algebraically independent polynomials in $k[x_1,\ldots,x_n]$. Assume that the homogeneous components of maximal deg…

Let $k[x_1,\ldots,x_n]$ be a polynomial ring, and let $f$ and $g$ be algebraically independent polynomials whose homogeneous components of maximal degree are algebraically dependen…