Definition:Matroid Induced by Algebraic Independence

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

Let $S \subseteq L$ be a finite subset of $L$.

Let $\mathscr I$ be the set of algebraically independent subsets of $S$.

Then $\struct{S, \mathscr I}$ is called the matroid induced by algebraic independence over $K$ on $S$.

Also see

 * Leigh.Samphier/Sandbox/Matroid Induced by Algebraic Independence is Matroid
 * Leigh.Samphier/Sandbox/Definition:Algebraic Matroid