Example of an ideal which is not principal in the ring $\mathbb{Z} [x]$
81982
Is $\mathbb{Z}[x]$ a principal ideal domain?
87078
Prove the following set is an ideal of the ring $Z[x]$
34183
An equivalent condition with $\{0\}$ being the only nilpotent ideal
121986
Do the Laurent polynomials over $\mathbb{Z}$ form a principal ideal domain?
84663
$A$ local Noetherian ring with principal maximal ideal implies PIR?
46303
Example of a non-Noetherian complete local ring
33245
Show that every ideal of the ring $\mathbb Z$ is principal
151786
Proving that there is no ideal $I$ in $\mathbb{Z}[t]$ such that $\mathbb{Z}[t]/I \cong \mathbb{Q}$
115920
Showing $R$ is a local ring if and only if all elements of $R$ that are not units form an ideal
17239
Find all ideals of ${\mathbb{Z}_n}$
144789
identify the ring $\mathbb{Z}[x]/(2x-1)$
87151
Primary ideals in Noetherian rings
6646
A (non-artificial) example of a ring without maximal ideals
92420
Characteristic of  a Non-unital Integral Ring
124864
A not free $\mathbb{Z}$-module
108896
Prime ideal in a polynomial ring over an integrally closed domain
1720
Show that $\langle 2,x \rangle$ is not a principal ideal in $\mathbb Z [x]$