Why is $(2,x)$ non-principal in $\Bbb Z[x]$?
1720
Show that $\langle 2,x \rangle$ is not a principal ideal in $\mathbb Z [x]$
33245
Show that every ideal of the ring $\mathbb Z$ is principal
121986
Do the Laurent polynomials over $\mathbb{Z}$ form a principal ideal domain?
19884
The units of $\mathbb Z_4[x]$
90276
Is $\sqrt{2}\in{\Bbb Z}[\sqrt{2}+\sqrt{3}]$ true?
75639
Showing that $\sqrt[3]{2}\notin\Bbb Q(\alpha_1,...,\alpha_k)$ where $\alpha_i^2\in\Bbb Q\ \forall i$
68838
Why $\sqrt[3]{3}\not\in \mathbb{Q}(\sqrt[3]{2})$?
24351
The ring $\Bbb Z\left [\frac{-1+\sqrt{-19}}{2}\right ]$ is not a Euclidean domain
89056
Intuitive understanding of ideal $I = (x+1,x^2+1)$ and the quotient $\Bbb Z[x]/I$
128711
$(\Bbb Z\oplus \Bbb Z)[X] \not\cong \Bbb Z[X]\oplus \Bbb Z[X]\,$?
78351
Why is $(2, 1+\sqrt{-5})$ not principal?
104789
How to tell an ideal of integer polynomial ring is principal?
104300
Help justifying that $\mathbb Q(\sqrt[3]{2})$ is not a splitting field over $\mathbb Q$.
147047
Does there exist a polynomial $p(x) \in \mathbb C[x]$ such that $p(x) \notin \mathbb R[x]$ and $p(x)p(-x)=p(x^2)$?
65536
Finitely generated ideals in a Boolean ring are principal, why?
132193
Why $\Bbb Z$ = (integers) is an integral domain?
148550
Units in quotient ring of $\mathbb Z[X]$