Sibling fields and algebras (reviewed)

Two finite separable extension fields $K_1$ and $K_2$ of a ground field $F$ are called siblings if they are not isomorphic, but have isomorphic Galois closures.

A finite dimensional separable $\Q$-algebra is isomorphic to a product of number fields. By its Galois closure, we mean the compositum of the Galois closures of the constituent fields. Then two algebras are siblings if they have isomorphic Galois closures, but are not isomorphic as $\Q$-algebras.