Definition:Algebraic Matroid

Definition

Let $L / K$ be a field extension.

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

Let $\struct{S, \mathscr I}$ be the matroid induced by Algebraic Independence over $K$ on $S$.

From Matroid Induced by Algebraic Independence is Matroid, $\struct{S, \mathscr I}$ is a matroid.

Then any matroid isomorphic to $\struct{S, \mathscr I}$ is called an algebraic matroid.

Also see

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

Sources

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