I found the injective hull of $k_R$ where $k$ is a field and $R$ is the ring of polynomials in $n$ commutative indeterminates in Lectures on modules and rings of T.Y. Lam. I don't know if there exists some result in case $R=k\langle x_1,...,x_n\rangle$ is the free $k$-algebra generated by $\{x_1,...,x_n\}$. Here is my question:
What is the injective hull of $k_R$ where $k$ is a field and $R=k\langle x_1,...,x_n\rangle$ is the free $k$-algebra generated by $\{x_1,...,x_n\}$?