Proof of No Unique Factorisation in $\mathbb Z[\sqrt{d}]$ for $d \leq-3$
24413
Why is $\mathbb{Z}[\sqrt{-n}], n\ge 3$ not a UFD?
55050
How to show that $\mathbb{Q}(i,\sqrt[4]{1+i} )$ is not contained in any cyclotomic extension of $\mathbb{Q}(i)$?
72144
Show that $\mathbb Q(\sqrt p) \not\simeq\mathbb Q(\sqrt q)$
117789
Computing Galois Group of $\mathbb{Q}(\sqrt{2},\sqrt{3}):\mathbb{Q}$
58009
How to show that $\mathbb Q(\sqrt 2)$ is not field isomorphic to $\mathbb Q(\sqrt 3).$
143067
Show given any $x\in\mathbb{R}$ show there exists a unique $n\in\mathbb{Z}$ such that $n-1\leq x <n$.
6171
Isomorphism between $\Bbb{Z}[\sqrt{d}]$ and a quotient of $\Bbb{Z}[X].$
44307
Prove $\sqrt[3]{3} \notin \mathbb{Q}(\sqrt[3]{2})$
37219
Quadratic Integers in $\mathbb Q[\sqrt{-5}]$
104300
Help justifying that $\mathbb Q(\sqrt[3]{2})$ is not a splitting field over $\mathbb Q$.
153069
Proof for Unique Factorization Domain
35874
Show that when $BA = I$, the solution of $Ax=b$ is unique
74224
On irreducible factors of $x^{2^n}+x+1$ in $\mathbb Z_2[x]$
86015
$\mathbb Q[x]/(x^2+1)$ is not isomorphic to $\mathbb Q[x]/(x^2+2)$
14003
$(\mathbb{Z}/2^n \mathbb{Z})^*$ is not cyclic Group for $n\geq 3$
35691
$\mathbb Z[\sqrt 3]$ contains infinitely many units
63313
Uniqueness of Powerseries in an arbitrarily small neighborhood of $0$ in $\mathbb C$