For which $r\in\mathbb{Q}$ is $\mathbb{Q}[x]/\langle x^2 - r\rangle$ a field?
85096
Let $K$ be a field and $f(x)\in K[x]$. Prove that $K[x]/(f(x))$ is a field if and only if $f(x)$ is irreducible in $K[x]$.
145279
Compute the (multiplicative) inverse of $4x+3$ in the field $\frac {\Bbb F_{11}[x]}{\langle x^2+1 \rangle}$?
45302
Finding the $\mathbb{Q}$-automorphisms of the splitting field of $x^p-2$ over $\mathbb{Q}$.
27086
proof for $\langle q| p \rangle = e^{ipq}$
78006
What is known about the quotient group $\mathbb{R} / \mathbb{Q}$?
14867
How to interpret $\langle x|\hat Q|x'\rangle$ for a quantum mechanical operator $\hat Q$?
111248
The Uniqueness of a Coset of $R[x]/\langle f\rangle$ where $f$ is a Polynomial of Degree $d$ in $R[x]$
53331
$\mathbb{Q}(\sqrt2, \sqrt3)$ is not isomorphic to $\mathbb{Q}(\sqrt[4]2)$
93328
$\mathbb{F}_p[X]/(X^2+X+1)$ is a field iff $p \equiv 2 \bmod 3$
19112
Ring $R= \mathbb Z_3[x]/\langle x^6-1\rangle$
120594
$\mathbb Z[i]/ \langle 1+2i \rangle \cong \mathbb Z_5$
99516
Show $\mathbb{Q}[\sqrt[3]{2}]$ is a field by rationalizing
63478
Is $\mathbb{Q}(\sqrt{2}) \cong \mathbb{Q}(\sqrt{3})$?
64878
Is this polynomial irreducible in $\mathbb{Q}$?
99884
Are $\mathbb{Q}_p$ and $\mathbb{Q}_q$ homeomorphic?
42332
Existence of multiplicative inverse in field $\mathbb{Q}(\sqrt{d})$
33025
What is the order of $(\mathbb{Z} \oplus \mathbb{Z})/ \langle (2,2) \rangle$ and is it cyclic?