Find the necessary and sufficient condition for $\mathbb{Q}(\sqrt{D_1})$ to be isomorphic to $\mathbb{Q}(\sqrt{D_2})$
47041
What are the conditions for integers $D_1$ and $D_2$ so that $\mathbb{Q}[\sqrt {D_1}] \simeq \mathbb{Q}[\sqrt {D_2}]$ as fields.
87160
Prove $\mathbb{Z}_3[x]/(x^2+1)$ and $\mathbb{Z}_3[x]/(x^2+x-1)$ are isomorphic.
93029
Prove that when $d$ is in $\mathbb{Q} \setminus\mathbb{Z}$, $\mathbb{Z}[\sqrt{d}]$ is not a finitely generated abelian group.
87682
Show that $\sqrt{2}\notin \mathbb{Q}(\sqrt[4]{3})$
27188
Bijection between $\mathbb{R}$ and $\mathbb{R}/\mathbb{Q}$
1914
General way to determine $\mathbb{Q}(\gamma) = \mathbb{Q}(\alpha,\beta)$ given $\alpha$ and $\beta$
91222
Isomorphism between $\mathfrak o(4,\mathbb R)$ and $\mathfrak o (3,\mathbb R) \oplus\mathfrak o (3,\mathbb R) $
84114
Does there exist a surjective homomorphism from $(\mathbb R,+)$ to $(\mathbb Q,+)$ ?
95459
$\mathbb{Q}(\sqrt{2+\sqrt{2}})$ is Galois over $\mathbb{Q}$?
127764
Showing that $\mathbb{Q}[\sqrt{2}, \sqrt{3}]$ contains multiplicative inverses
93169
Show that $(\mathbb Z[x],+)$ and $(\mathbb Q_{>0},\cdot)$ are isomorphic groups
35216
Prove $\mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5}):\mathbb{Q}$ is a simple extension
4228
Prove that the only automorphism of $\mathbb{Q}(\sqrt[3]{2})$ is the identity automorphism.
109610
Is $\mathbb{R}[X]/(P)$ isomorphic to $\mathbb C$ for every irreducible polynomial $P$ of degree $2?$
98496
Let $a,b \in \mathbb{Q^{+}}$ then $\sqrt{a} + \sqrt{b} \in \mathbb{Q} $ iff $\sqrt{a} \in \mathbb{Q}$ and $\sqrt{b} \in \mathbb{Q}$
157496
Determine the Galois group of $\mathbb{Q}(\sqrt{a+b\sqrt{d}})$
1020
Proving that $\mathbb{Z}[\sqrt{2}]$ is a Euclidean domain