$\mathbb{Z}[\frac{1-\sqrt{-19}}{2}]$ - principal ring, but not an euclidean ring
136855
Proof that $\mathbb{Z}\left[\frac{1 + \sqrt{-19}}{2}\right]$ is a PID
113152
Prove Principal Ideal Domain from Bezout's condition, and terminating divisibility chain
144789
identify the ring $\mathbb{Z}[x]/(2x-1)$
147871
How do the prime ideals of $\mathbb{Z}_{k}$ look like?
1720
Show that $\langle 2,x \rangle$ is not a principal ideal in $\mathbb Z [x]$
62183
Find the quotient field of $\mathbb{Z}[\sqrt {2}]$
155745
Ideals of $\mathbb{Z}[X]$
52081
Why is not the ring $\mathbb{Z}[2\sqrt{2}]$ a unique factorization domain?
93029
Prove that when $d$ is in $\mathbb{Q} \setminus\mathbb{Z}$, $\mathbb{Z}[\sqrt{d}]$ is not a finitely generated abelian group.
104789
How to tell an ideal of integer polynomial ring is principal?
19310
Identify the ring $\mathbb{Z}[x]/(2x)$
80679
Principal ideal rings that are not integral domains
33245
Show that every ideal of the ring $\mathbb Z$ is principal
30401
Determining the structure of the quotient ring $\mathbb{Z}[x]/(x^2+3,p)$
149973
Showing the following coordinate rings are not isomorphic
148550
Units in quotient ring of $\mathbb Z[X]$
61383
How do I see that every left ideal of a square matrix ring over a field is principal?