Show that the Gauss ring $\mathbb{Z}[i]$ is Euclidean ring
23721
Prove that the Gaussian Integer's ring is a Euclidean domain
112043
Show that the ideal $ (2, 1 + \sqrt{-7} ) $ in $ \mathbb{Z} [\sqrt{-7} ] $ is not principal
73402
Showing that $(\mathbb{Z}/p^{a}\mathbb{Z})^*$ is a cyclic group
145630
What is the ideal class group of the ring $\mathbb{R}[x,y]/(x^2+y^2-1)$?
1719
Ideals in the ring of Gaussian integers
149856
Image of ring homomorphism is a subring
6121
Quotient ring of Gaussian integers
21840
Zero divisors and units for the ring $\mathbb{Z}/n\mathbb{Z}$ with integer $n$
147871
How do the prime ideals of $\mathbb{Z}_{k}$ look like?
109691
When are kernels of homomorphisms on $\mathbb{Z}[x]$ principal ideals, and what does this have to do with Gauss's lemma?
135303
Formal power series are a euclidean ring
56779
The norm of a Gaussian prime is a prime or a square of a prime in $\mathbb{Z}$
87078
Prove the following set is an ideal of the ring $Z[x]$
154845
Irreducible elements in  $\mathbb{Z}[\sqrt{-2}]$ and is it a Euclidean domain?
77903
Finding the integral closure of $\mathbb{Z}$ in $\mathbb{Q}[i]$
124864
A not free $\mathbb{Z}$-module
54585
Order of some quotient ring of Gaussian integers