nLab algebraically independent subset

Idea

Let $L$ be a field, let $K \subseteq L$ be a subfield of $K$, and let $S \subseteq L$ be a subset of $L$. Then $S$ is algebraically independent from $K$ if for every element $\alpha \in S$, every polynomial function with coefficients in $K$ is equal to the zero polynomial function if it has $\alpha$ among its roots when interpreted in $L$ (in other words, $\alpha$ is transcendental over $K$).

Related concepts

• transcendental element

• transcendental extension

• linearly independent subset

 References

• Wikipedia, Algebraic independence