Proving a subring of $\mathbb{Q}$ containing $\mathbb{Z}$ is a PID
21747
A subring of the field of fractions of a PID is a PID as well.
124864
A not free $\mathbb{Z}$-module
41035
Mapping that proves $\mathbb{Z} \subset \mathbb{Q}$
149783
$\mathbb Z\times\mathbb Z$ is principal but is not a PID
93621
Prove that $\mathbb{Z}[\omega]$ is an integral domain
119056
If in a UFD every maximal ideal is principal then it is a PID
42213
Computing $\text{Gal}(\mathbb{Q}^{ab}/\mathbb{Q})$
6171
Isomorphism between $\Bbb{Z}[\sqrt{d}]$ and a quotient of $\Bbb{Z}[X].$
24224
How to prove the ring of Laurent polynomials over a field is a principal ideal domain?
76501
How can we show that $\mathbb Q$ is not a free $\mathbb Z$-module?
57669
A proof that $\mathbb{Z}_{p}$ is an integral domain if and only if $p$ is prime.
9129
Show that $\mathbb{Q}(\zeta_n)$ is Galois over $\mathbb{Q}$ and $Gal(\mathbb{Q}(\zeta_n)/\mathbb{Q}))\cong \mathbb{Z_n}^*$
135611
Extensions of $\mathbb{Z}$ by $\mathbb{Z}$
136855
Proof that $\mathbb{Z}\left[\frac{1 + \sqrt{-19}}{2}\right]$ is a PID
30401
Determining the structure of the quotient ring $\mathbb{Z}[x]/(x^2+3,p)$
115541
Subrings of polynomial rings over the complex plane
64130
Prove that $\mathbb{Q}^{\times}$ not isomorphic to $\mathbb{Z}^{n}$