A finite field $F$ such that $F[\sqrt{2}]$ and $F[\sqrt{3}]$ are not isomorphic (as fields)
141418
When is $\mathbb{F}_p[x]/(x^2-2)\simeq\mathbb{F}_p[x]/(x^2-3)$ for small primes?
99516
Show $\mathbb{Q}[\sqrt[3]{2}]$ is a field by rationalizing
142352
how to prove $G_1$ and $G_2$ aren't isomorphic?
145140
Subfield of $\mathbb{Q}(\sqrt[n]{a})$
44307
Prove $\sqrt[3]{3} \notin \mathbb{Q}(\sqrt[3]{2})$
78350
When does a finite ring become a finite field?
11564
$\mathbb{Q}(\sqrt{p},\sqrt[3]{q})=\mathbb{Q}(\sqrt{p}\sqrt[3]{q})$ for distinct prime $p,q$
140106
How to prove a finite field is not ordered?
84017
Is $\sqrt[3]{2}$ contained in $\mathbb{Q}(\zeta_n)$?
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
92703
Proving that $\mathbb{Z}[x]$ and $\mathbb{Q}[x]$ are not isomorphic.
94326
a square in a finite field of odd order
146334
Are there fields $F$ such that the rings $F[x]/(x^2)$ and $F[x]/(x^2-1)$ are isomorphic?
153444
$\mathbb{Q}(\sqrt[3]{2})$ is not in any cyclotomic extension of $\mathbb{Q}$
42332
Existence of multiplicative inverse in field $\mathbb{Q}(\sqrt{d})$
103654
A finite field extension that is not simple
119305
Is the splitting field equal to the quotient $k[x]/(f(x))$ for finite fields?