Question on finitely presented algebra

Question

Suppose $S$ is a finitely presented $R$-algebra. If $g:R[x_1, \ldots, x_n] \to S$ is surjective, then $\ker(g)$ is finitely generated.

We can write $S$ as $R[y_1, \ldots, y_m]/(f_1,\ldots,f_t)$ and write $g$ as $g:R[x_1,\ldots,x_n] \to R[y_1, \ldots, y_m]/(f_1,\ldots,f_t)$, but I don't know how to find the kernel.

Answer 1

This is stated and proved at http://stacks.math.columbia.edu/tag/00R2.