Let $A \subset B$(integral domain), $B$ is finitely generated over $A$. Let $y_1, \cdots, y_n \in B$ algebraically independent over $A$. Then homomorphism $f:A \to \Omega$(algebraically closed field) can be extended to $A[y_1,\cdots,y_n] \to \Omega$ by $y_i \mapsto 0$ for all $i$.
How can I prove it other than by using direct method? Is there any theorem or generalization? (I skimmed serge lang but failed to find similar one, all theorems looks slightly different.)
How about the case of $y_1, \cdots, y_n$ algebraically dependent?