# separable closure

Let $K$ be a field and let $L$ be an algebraic closure of $K$. The separable closure of $K$ inside $L$ is the compositum of all finite separable extensions of $K$ contained in $L$ (that is to say, the smallest subfield of $L$ that contains every finite separable extension of $K$).

Title separable closure SeparableClosure 2013-03-22 12:12:11 2013-03-22 12:12:11 djao (24) djao (24) 6 djao (24) Definition msc 12F10