Yes/No :Is $ \mathbb{Q}( \sqrt[3] 2)$ a normal extension of $\mathbb{Q}?$
104300
Help justifying that $\mathbb Q(\sqrt[3]{2})$ is not a splitting field over $\mathbb Q$.
75639
Showing that $\sqrt[3]{2}\notin\Bbb Q(\alpha_1,...,\alpha_k)$ where $\alpha_i^2\in\Bbb Q\ \forall i$
43300
The degree of $\sqrt{2} + \sqrt[3]{5}$ over $\mathbb Q$
11564
$\mathbb{Q}(\sqrt{p},\sqrt[3]{q})=\mathbb{Q}(\sqrt{p}\sqrt[3]{q})$ for distinct prime $p,q$
75349
Minimal polynomial of $\sqrt[3]{2} + \sqrt{3}$
74663
Is $\mathbb{R}$ an algebraic extension of some proper subfield?
135611
Extensions of $\mathbb{Z}$ by $\mathbb{Z}$
24413
Why is $\mathbb{Z}[\sqrt{-n}], n\ge 3$ not a UFD?
142470
$\mathbb{Q}(\sqrt{p},\sqrt[3]{q})= \mathbb{Q}(\sqrt{p}\cdot \sqrt[3]{q})$ ??
27440
Is normal extension of normal extension always normal?
81944
Galois representations and normal bases
145140
Subfield of $\mathbb{Q}(\sqrt[n]{a})$
68790
Do we have $K(\beta)=K(\beta^2)$ for field extension of odd degree?
133312
Are these polynomials irreducible in $\mathbb{Q}[x]$?
58009
How to show that $\mathbb Q(\sqrt 2)$ is not field isomorphic to $\mathbb Q(\sqrt 3).$
39642
Efficient way to find $[\mathbb{Q}(\sqrt{5}, \sqrt{3}, \sqrt{2}): \mathbb{Q}(\sqrt{3}, \sqrt{2})]$
16163
Show $\mathbb{Q}(\sqrt{2},\sqrt{3})$ is a simple extension field of $\mathbb{Q}$.