Let $K=\mathbb Q[i]$. Show that $K(\sqrt[4]{1+i})$ does not lie in any cyclotomic extension of $K$.
55050
How to show that $\mathbb{Q}(i,\sqrt[4]{1+i} )$ is not contained in any cyclotomic extension of $\mathbb{Q}(i)$?
40626
Suppose that $ a,b \in \mathbb{Z}$ If 4 divides $ a^2 + b^2$, then $a$ and $b$ are not odd.
76501
How can we show that $\mathbb Q$ is not a free $\mathbb Z$-module?
85032
$Q(\mathbb{Z}[t]) / \mathbb{Z}[t]$ is not injective
98731
Show that there is no epimorphism from ($\mathbb{Q}$, +) to ($\mathbb{Z}$, +)
127764
Showing that $\mathbb{Q}[\sqrt{2}, \sqrt{3}]$ contains multiplicative inverses
85586
Proving $\mathbb{Q}$ isn't homeomorphic to $\mathbb{Z}$
38549
$\mathbb{Q}(\sqrt{n}) \cong \mathbb{Q}(\sqrt{m})$ iff $n=m$
126927
$\mathbb Q$ is not the direct product of two non-trivial groups.
53660
Show that $ a，b，c, \sqrt{a}+ \sqrt{b}+\sqrt{c} \in\mathbb Q  \implies  \sqrt{a},\sqrt{b},\sqrt{c} \in\mathbb Q $
16163
Show $\mathbb{Q}(\sqrt{2},\sqrt{3})$ is a simple extension field of $\mathbb{Q}$.
98496
Let $a,b \in \mathbb{Q^{+}}$ then $\sqrt{a} + \sqrt{b} \in \mathbb{Q} $ iff $\sqrt{a} \in \mathbb{Q}$ and $\sqrt{b} \in \mathbb{Q}$
24168
A characterisation of quadratic extensions contained in cyclic extensions of degree 4
97258
Give $\ker(\phi)$ for $\phi: \mathbb{Z} \to \mathbb{Z_7}$ such that $\phi(1)=4$
44307
Prove $\sqrt[3]{3} \notin \mathbb{Q}(\sqrt[3]{2})$
31216
Is the image of $\Phi_n(x) \in \mathbb{Z}[x]$ in $\mathbb{F}_q[x]$ still a cyclotomic polynomial?
132386
Show that $(\mathbb{Q}^*,\cdot)$ and $(\mathbb{R}^*,\cdot)$ aren't cyclic