Hi all

Quick question that I think is true but haven't been able to prove.

Suppose there is a subring $R \subset k[x_1, \ldots, x_r]$ containing field $k$ and generated by homogenous polynomials $p_1, \ldots, p_t$. Now assume the radical of the homogenous ideal of $k[x_1, \ldots, x_k]$ generated by the $p_i$ is the maximal ideal $(x_1, \ldots, x_r)$. Then the transcendence degree of $R$ over $k$ is $r$.