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.

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- Last edited by John Jones on 2018-08-02 00:07:49

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- 2018-08-02 00:07:49 by John Jones (Reviewed)