This is related to Ueno, Algebraic Geometry 2, Example 5.28.
Let $R=k[x_1,\dots, x_n]$ and $I=(x_1,\dots, x_n)\subset R$. Let $S=R\oplus I\oplus I^2\oplus I^3\oplus\dots$ be graded $R-$algebra.
Consider $R[y_0,\dots, y_{n-1}]\to S$ by $f(y_0,\dots, y_n)\to f(x_1,\dots, x_n)$ is clearly surjective graded ring homomorphism.
It is clear that kernel contains $x_iy_j-y_ix_j\in R[y_0,\dots, y_{n-1}]$.
$\textbf{Q:}$ Is it true that kernel is exactly generated by $(x_iy_j-y_ix_j|i,j)$ for all $i,j$? If so, is there an easy way to check this?