Definition:Algebraically Independent

Definition
Let $L/K$ be a field extension.

Let $A \subseteq L$ be a subset of $L$.

Let $K \left({\left\{{X_\alpha}\right\}_{\alpha \in A}}\right)$ be the Field of Rational Functions in the indeterminates $\left\{{X_\alpha : \alpha \in A}\right\}$.

Then $A$ is algebraically independent over $K$ if there exists a homomorphism:
 * $\phi: K \left({\left\{{X_\alpha}\right\}_{\alpha \in A}}\right) \to L$

such that:
 * $\phi \left({X_\alpha}\right) = \alpha$