Show that $\mathbb{Z}\left[\frac{1+\sqrt{-3}}{2}\right]$ is a Euclidean Domain.
55396
Prove that the class number of $\mathbb{Z}[\zeta_3]$ is $1$
63478
Is $\mathbb{Q}(\sqrt{2}) \cong \mathbb{Q}(\sqrt{3})$?
17859
Showing $F[x,y]/(ax^2+by^2-1)$ is a Dedekind domain
19230
Prime/Maximal Ideals in $\mathbb{Z}[\sqrt d]$
75639
Showing that $\sqrt[3]{2}\notin\Bbb Q(\alpha_1,...,\alpha_k)$ where $\alpha_i^2\in\Bbb Q\ \forall i$
88425
Prove that $\,\sqrt [n] n < 1 + \sqrt{\frac{2}{n}}\,$
135303
Formal power series are a euclidean ring
17161
Can anyone make me understand in simple language why the second condition for being an Euclidean domain is superfluous?
116453
Is any quotient of a Euclidean domain by a prime ideal a Euclidean domain?
57670
Show that $|z_1 + z_2|^2 < (1+C)|z_1|^2 + \left(1 + \frac{1}{C}\right) |z_2|^2$
87682
Show that $\sqrt{2}\notin \mathbb{Q}(\sqrt[4]{3})$
66238
Proving $\mathbb{Z}[\sqrt {10}]$ is not a UFD
58717
Why isn't $\mathbb Z [\sqrt{pq}]$ a factorial domain
13174
Show that $A[X]/(aX+b)$ is an integral domain
125680
Show that $(1+u) \log (1+u) - u \ge \frac{u^2}{2(1+u/3)} $
94579
$\mathbb{Q}[x,y]/\langle x^2+y^2-1 \rangle$ is an integral domain, and its field of fractions is isomorphic to $\mathbb Q(t)$
23721
Prove that the Gaussian Integer's ring is a Euclidean domain