Show that $\mathbb{Z}[\sqrt{-2}]$ is unique factorization domain.
1020
Proving that $\mathbb{Z}[\sqrt{2}]$ is a Euclidean domain
57669
A proof that $\mathbb{Z}_{p}$ is an integral domain if and only if $p$ is prime.
71572
factor-square property (FSP) of polynomials
87617
Ring of $\mathbb{Z}_2$-valued functions
58717
Why isn't $\mathbb Z [\sqrt{pq}]$ a factorial domain
50930
Proving the continued fraction representation of $\sqrt{2}$
93291
Method for determining irreducibles and factorising in $\mathbb Z[\sqrt{d}]$
92517
Easy way to show that $\mathbb{Z}[\sqrt[3]{2}]$ is the ring of integers of $\mathbb{Q}[\sqrt[3]{2}]$
154845
Irreducible elements in  $\mathbb{Z}[\sqrt{-2}]$ and is it a Euclidean domain?
85987
Prove that $k[x,y,z,w]/(xy-zw)$, the coordinate ring of $V(xy-zw) \subset \mathbb{A}^4$, is not a unique factorization domain
22789
How to determine whether a unique factorization domain is a principal ideal domain?
129834
Show that there is a unique polynomial of degree at most $2n+1$ such that $q^{[k]}(x_1)=a_k,$ $q^{[k]}(x_2)=b_k$ for $k=0, \dots, n$.
31933
$x^2 = 1$ in the ring $\mathbb{Z}/n \mathbb{Z}$
53331
$\mathbb{Q}(\sqrt2, \sqrt3)$ is not isomorphic to $\mathbb{Q}(\sqrt[4]2)$
113152
Prove Principal Ideal Domain from Bezout's condition, and terminating divisibility chain
125604
Proof that $\mathbb{Z}$ has no zero divisors
38364
Showing that $x^n -2$ is irreducible in $\mathbb{Q}[X]$