Prove that $\mathbb{Z}_5$ is a field
7899
Show that if $p$ is prime then $\Bbb Z_p$ is a field
137858
Showing that $\mathbb{Z}[i]/I$ is a finite field whenever $I$ is a prime ideal, and also finding its cardinality?
99516
Show $\mathbb{Q}[\sqrt[3]{2}]$ is a field by rationalizing
91113
$ \exists a, b \in \mathbb{Z} $ such that $ a^2 + b^2 = 5^k $
10111
Prove or disprove that Q[√2] is a field
41050
Degree of the splitting field of $ x^3-5 $ over $\mathbb{Q}$
134896
Enlightening proof that the algebraic numbers form a field
146617
A complete picture of the lattice of subfields for a cyclotomic extension over $\mathbb{Q}$.
109801
multiplicative group of infinite fields
9129
Show that $\mathbb{Q}(\zeta_n)$ is Galois over $\mathbb{Q}$ and $Gal(\mathbb{Q}(\zeta_n)/\mathbb{Q}))\cong \mathbb{Z_n}^*$
138911
Is $\mathbb R^2$ a field?
114152
Intermediate fields between $\mathbb{Z}_2 (\sqrt{x},\sqrt{y})$ and $\mathbb{Z}_2 (x,y)$
103817
Find splitting field of $x^5-4x+2$ over $\mathbb{Q}$
52800
Show that $z^5-1=(z-1)(z^2+2z\cos{\pi \over 5}+1)(z^2-2z\cos{2\pi \over 5}+1)$
120699
Is $\mathcal{O}_{\mathbb{Q}(\sqrt{5})} = \mathbb{Z}[\phi]$?
70981
Galois Group of $x^5+1$
93328
$\mathbb{F}_p[X]/(X^2+X+1)$ is a field iff $p \equiv 2 \bmod 3$