Let $k$ be a field of characteristic zero.
Let $R=k\big[z_1,...,z_p\big]$ a $k$-algebra of finite type which is a domain. Let $F$ be its field of fractions and $x_1,...,x_n$ a transcendence basis of $F$ over $k$ which verifies: $\forall i\in\{1,...,n\},\,x_i\in R$.
Show that $\forall j\in\{1,...,p\},\,z_j$ is algebraic over $k(x_1,...,x_n)$.
Can you help please.
Thank you in advance.