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

• Matroid Induced by Algebraic Independence is Matroid
• Definition:Algebraic Matroid

Sources

• 1976: Dominic Welsh: Matroid Theory Chapter $11$. $\S 1$. Algebraic matroids