Algebraic Number Theory
《Algebraic Number Theory》 · 第 399 页 · Chapter VI，Section 6「Global Class Fields」，Proposition 6.8 后定义段
The Hilbert class field, or more precisely the small Hilbert class field, is the maximal unramified abelian extension $H/K$ in which all infinite places split completely; its Galois group is canonically isomorphic to the ideal class group.