Definition:Algebraically Independent

Definition
Let $L/K$ be a field extension and $A \subseteq L$ a subset.

Let $K(\{X_\alpha\}_{\alpha \in A})$ be the field of rational functions in the indeterminates $\{X_\alpha : \alpha \in A\}$.

Then $A$ is algebraically independent over $K$ if there exists a homomorphism $K(\{X_\alpha\}_{\alpha \in A}) \to L$ sending $X_\alpha$ to $\alpha$.