Let \(L/k\) be an algebraic field extension, let \(\bar{k}\) be an algebraic closure of \(k\), and fix an embedding \(\sigma\colon k\embeds \bar{k}\). The separable degree \([L:k]_s\) is the cardinality of the set of field embeddings \(\sigma'\colon L\to \bar{k}\) that extend \(\sigma\), that is, with \(\sigma'|_k=\sigma\):
Here \(\iota\colon k\embeds L\) is the inclusion.