Consider an extension $K/F$. Suppose $S \subset K$ such that $S$ is algebraically independent over $F$. Prove that each $s \in S$ is transcendental over $F(S-\{s\})$.
How do I prove this claim? Any help will be appreciated.
Consider an extension $K/F$. Suppose $S \subset K$ such that $S$ is algebraically independent over $F$. Prove that each $s \in S$ is transcendental over $F(S-\{s\})$.
How do I prove this claim? Any help will be appreciated.