About $\mathbb Z_{p}[\sqrt{k}]$, when is it a field?
131971
If $k>0$ is a positive integer and $p$ is any prime, when is $\mathbb Z_p[\sqrt{k}] =\{a + b\sqrt k~|~a,b \in\mathbb Z_p\}$ a field.
153204
Euclidean domain $\mathbb{Z}[\sqrt{d}]$
78835
An automorphism of the field of $p$-adic numbers
98256
Subfields of $\mathbb{Q}(\sqrt{2},\sqrt{3})$
46565
Show that $\mathbb{Q}(\sqrt{2})$ is a field.
155125
Every ordered field has a subfield isomorphic to $\mathbb Q$?
133775
Is $\mathbb{Z}[\sqrt{-7}]$ a UFD or not?
137278
Quotient field of gaussian integers
84017
Is $\sqrt[3]{2}$ contained in $\mathbb{Q}(\zeta_n)$?
133636
Is $\mathbb Z[X]/(X^2-1)$ a domain?
104300
Help justifying that $\mathbb Q(\sqrt[3]{2})$ is not a splitting field over $\mathbb Q$.
75828
Compute Galois group of $\mathbb F_q/\mathbb F_p$
58717
Why isn't $\mathbb Z [\sqrt{pq}]$ a factorial domain
8087
Algebraic integers of $\mathbb{Q}(\sqrt{m})$ for $m$ a squarefree integer
99884
Are $\mathbb{Q}_p$ and $\mathbb{Q}_q$ homeomorphic?
42332
Existence of multiplicative inverse in field $\mathbb{Q}(\sqrt{d})$
76501
How can we show that $\mathbb Q$ is not a free $\mathbb Z$-module?