Prove $\mathbb{Z} [\sqrt{2}]$ is a Euclidean ring.
1020
Proving that $\mathbb{Z}[\sqrt{2}]$ is a Euclidean domain
146470
Show $\mathbb{Z}[\sqrt{6}]$ is a Euclidean domain
84017
Is $\sqrt[3]{2}$ contained in $\mathbb{Q}(\zeta_n)$?
52081
Why is not the ring $\mathbb{Z}[2\sqrt{2}]$ a unique factorization domain?
35216
Prove $\mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5}):\mathbb{Q}$ is a simple extension
127764
Showing that $\mathbb{Q}[\sqrt{2}, \sqrt{3}]$ contains multiplicative inverses
92583
Prove that $N(\gamma) = 1$ if, and only if, $\gamma$ is a unit in the ring $\mathbb{Z}[\sqrt{n}]$
13983
Show that If $R[X]$ is Euclidean domain then $R$ is a field
135303
Formal power series are a euclidean ring
32772
Proving units in a ring
138944
Is $\mathbb Z[\sqrt{-3}]$ Euclidean under some other norm?
6121
Quotient ring of Gaussian integers
112043
Show that the ideal $ (2, 1 + \sqrt{-7} ) $ in $ \mathbb{Z} [\sqrt{-7} ] $ is not principal
41878
Cardinal of quotient rings of gaussian integers.
69373
Prove that $(0)$ is a radical ideal in $\mathbb{Z}/n\mathbb{Z}$ iff $n$ is square free
116943
Proof for maximal ideals in $\mathbb{Z}[x]$
149519
Prove that a Boolean ring is a Bezout ring .