Why is $I[x]$ not maximal $\mathbb{Z}[x]$?
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 $\mathbb Z$?
57310
Prove $\mathbb{Z}$ is not a vector space over a field
23837
Why is $\mathbb{R}/{\sim}$ not first countable at $[0]$, where $x \sim y \Leftrightarrow x = y\text{ or }x,y \in \mathbb{Z}$?
120181
The ideal generated by $2$ and $ x$ in $\mathbb{Z}[x]$
144245
Shorter proof of $R/I$ is a field if and only if $I$ is maximal
1720
Show that $\langle 2,x \rangle$ is not a principal ideal in $\mathbb Z [x]$
133636
Is $\mathbb Z[X]/(X^2-1)$ a domain?
104562
Prove that $\mathbb{Z}$ is not isomorphic to additive group of any vector space over any field.
56171
Is $K(X)$ never algebraically closed?
52081
Why is not the ring $\mathbb{Z}[2\sqrt{2}]$ a unique factorization domain?
26749
$\mathbb{Z}[X]/(X^2-1)$ is not isomorphic with $\mathbb{Z}\times \mathbb{Z}$
79056
Prove that $\mathbb Z^n$ is not isomorphic to $\mathbb Z^m$ for $m\neq n$
76661
Checking the maximality of a principal ideal in $R[x]$
151786
Proving that there is no ideal $I$ in $\mathbb{Z}[t]$ such that $\mathbb{Z}[t]/I \cong \mathbb{Q}$
74537
Maximal Ideals in $K[y]$
6307
maximal ideal not containing some expression
93723
Find all the maximal ideals in the ring $\mathbb{R}[x]$.