Separable degree

Summary

The separable degree $[L:K]_s$ of an algebraic extension $L/K$ counts the embeddings of $L$ into an algebraically closed field. Only the embeddings that extend a fixed embedding of $K$ are counted. For a finite extension it divides the degree $[L:K]$, and the quotient is a power of the characteristic exponent, called the inseparable degree. It equals $[L:K]$ exactly when $L/K$ is separable, and it equals the degree of the separable closure of $K$ in $L$. It measures how much of an extension is visible to Galois theory.