# Galois closure

Let $K$ be an extension field of $F$. A Galois closure of $K/F$ is a field $L\supseteq K$ that is a Galois extension of $F$ and is minimal in that respect, i.e. no proper subfield of $L$ containing $K$ is normal over $F$.

Title Galois closure GaloisClosure 2013-03-22 13:09:34 2013-03-22 13:09:34 scanez (1021) scanez (1021) 6 scanez (1021) Definition msc 12F10