We know that in general Normal extension of a Normal extension may not be normal. I want an example where it holds, i.e Normal extension of a Normal extension is still Normal. Is there any example of such extension ?
Thank you.
2026-02-23 02:48:21.1771814901
Example of an extension where Normal of a Normal extension is Normal.
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Here is a non-trivial example: For $\mathbb Q\subset \mathbb Q(\sqrt 2)\subset \mathbb Q(\sqrt 2,\sqrt 3)$ all the three extensions
$\mathbb Q\subset \mathbb Q(\sqrt 2)$
$\mathbb Q\subset \mathbb Q(\sqrt 2,\sqrt 3)$
$ \mathbb Q(\sqrt 2)\subset \mathbb Q(\sqrt 2,\sqrt 3)$
are Galois (and thus normal) extensions