Show that $\mathbb{Q}[\sqrt{7}]$ is a field of fractions of $\mathbb{Z}[\sqrt{7}]$
62183
Find the quotient field of $\mathbb{Z}[\sqrt {2}]$
118299
Show that $(\mathbb{Z}[x]/(x^{n+1}))^{\times}\cong \mathbb{Z}/2\mathbb{Z}\times\Pi_{i=1}^n\mathbb{Z}$
114152
Intermediate fields between $\mathbb{Z}_2 (\sqrt{x},\sqrt{y})$ and $\mathbb{Z}_2 (x,y)$
101164
Show that $B \cong \mathbb Z /2\mathbb Z$ for a Boolean field B
98577
Show that the set $\mathbb{Q}(\sqrt{p})=\{a+b\sqrt{p}; a,b,p\in\mathbb{Q},\sqrt{p}\notin \mathbb{Q}\}$ is a field
87467
Finding some missing subfields of a splitting field of $x^4-7$
122932
When $(\mathbb{Q}(\zeta_n) : \mathbb{Q}) = 2$?
40400
Finding an isomorphism between $\mathbb{Z}[i]/(7)$ and $\mathbb{Z}[\sqrt{-2}]/(7)$
72144
Show that $\mathbb Q(\sqrt p) \not\simeq\mathbb Q(\sqrt q)$
104300
Help justifying that $\mathbb Q(\sqrt[3]{2})$ is not a splitting field over $\mathbb Q$.
27021
Show that $Q[\sqrt3]$ is a field
3317
Subgroup generated by $2$ and $7$ in $(\mathbb Z,+)$
58009
How to show that $\mathbb Q(\sqrt 2)$ is not field isomorphic to $\mathbb Q(\sqrt 3).$
3711
Finding the intermediate fields of $\Bbb{Q}(\zeta_7)$.
73412
Splitting field of $x^6+x^3+1$ over $\mathbb{Q}$
9129
Show that $\mathbb{Q}(\zeta_n)$ is Galois over $\mathbb{Q}$ and $Gal(\mathbb{Q}(\zeta_n)/\mathbb{Q}))\cong \mathbb{Z_n}^*$
78416
Show that $7$ divides $a^{15}-a^3$ for any integer $a$