Find $\alpha$ such that the given field is $\mathbb{Q}(\alpha)$
32760
Is $\mathbf{Q}(\sqrt{2}, \sqrt{3}) = \mathbf{Q}(\sqrt{2}+\sqrt{3})$?
76685
Determine $\text{Aut}(S)$ where $S = \mathbb{Q}[x]/(x^2)$
51021
Find all the intermediate fields of the splitting field of $x^4 - 2$ over $\mathbb{Q}$
99835
Polynomial in $\mathbb{Q}[x]$ with root $\sqrt[3]{2}+\sqrt[3]{3}$
133870
if $\alpha\leq\beta$ then there is $\gamma$ such as $\alpha+\gamma=\beta$
127002
Prove that for a nonzero element $a$ of a field $F$ with $q$ elements $a^{-1} = a^{q-2}$
114295
Find all the middle fields of the splitting field of $x^4-2$ over $\mathbb{Q}$
24919
$\mathbb{Q}(\zeta_{10}) $ degree of field extension over $\mathbb{Q}$
27278
Let $\alpha \in \overline{\Bbb Q}$ a root of $X^3+X+1\in\Bbb Q[X]$. Calculate the minimum polynomial of $\alpha^{-1}$ en $\alpha -1$.
134619
Galois extension with $X^4-2aX^2+b\in\mathbb Q[X]$
54267
Field of fractions of $\mathbb{Q}[x,y]/\langle x^2+y^2-1\rangle$
95602
Computing the Galois group of $x^4+ax^2+b \in \mathbb{Q}[x] $
50668
Show that $\mathbb{Q}(\sqrt2, \sqrt[3]2)$ is a primitive field extension of $\mathbb{Q}$.
118310
How to find $\operatorname{Gal}(S/\mathbb{Q})$
50172
Show that $\mathbb{Q}(\sqrt{2})$ is the smallest subfield of $\mathbb{C}$ that contains $\sqrt{2}$
622
Galois Group of $\sqrt{2+\sqrt{2}}$ over $\mathbb{Q}$
157496
Determine the Galois group of $\mathbb{Q}(\sqrt{a+b\sqrt{d}})$