Why $I=\left\{p(x)\in \mathbb{Z}\left[X\right]:2\mid p(0)\right\}$ is not a principal ideal?
1720
Show that $\langle 2,x \rangle$ is not a principal ideal in $\mathbb Z [x]$
129302
Proving whether ideals are prime in $\mathbb{Z}[\sqrt{-5}]$
111996
Maximal and Prime Ideal in Z
122012
The ideal $(x,y)$ is not a free $K[x,y]$-module
138114
Proving the quotient of a principal ideal domain by a prime ideal is again a principal ideal domain
99198
Principal ideal and free module
20296
The ideal $I= \langle x,y \rangle\subset k[x,y]$ is not principal
17075
Show an Ideal is the principal ideal for some polynomial.
149203
Symbolic power of a prime ideal is primary
104789
How to tell an ideal of integer polynomial ring is principal?
24224
How to prove the ring of Laurent polynomials over a field is a principal ideal domain?
42875
The prime elements of the ring $ \mathbb{Z} \! \left[ \dfrac{i \sqrt{3} - 1}{2} \right] $.
133975
Localising a polynomial ring and non-maximal prime ideal
60665
Meaning of $\mathbb{Z}\left[\sqrt{3}\right]$?
116430
If $I = \langle 2\rangle$, why is $I[x]$ not a maximal ideal of $\mathbb Z[x]$, even though $I$ is a maximal ideal of $\mathbb Z$?
76661
Checking the maximality of a principal ideal in $R[x]$
148208
In Noetherian ring $R$, ideal $I\subset R$, $P\in\mathrm{Ass}(I),P=I:a$ for some $a\in R$.