Let $I=\langle 4, 2x,x^{2} \rangle$ in $\mathbb{Z[x]}$. Show that $I$ can not be generated by 2 elements.
104486
Ideal in $\mathbb Z[x]$ which is not two-generated
120940
An irreducible polynomial in a subfield of $\mathbb{C}$ has no multiple roots in $\mathbb{C}$
132725
Is $\mathbb{Z}/\langle n\rangle$ cyclic and of order $n$?
134687
Is there a more elegant way of proving $\langle (1,2)(3,4), (1,2,3,4,5) \rangle = A_5$
85586
Proving $\mathbb{Q}$ isn't homeomorphic to $\mathbb{Z}$
120594
$\mathbb Z[i]/ \langle 1+2i \rangle \cong \mathbb Z_5$
140405
Show that there does not exist any $n$ for which $a^n=a$ forall $a\in \Bbb Z_m$ where $m$ is divisible by the square of some prime.
124438
Find $|(\mathbb{Z} \oplus \mathbb{Z}) / \langle(3,6)\rangle|$ and determine if its cyclic
102721
Number of elements in the ring $\mathbb Z [i]/\langle 2+2i\rangle$
111248
The Uniqueness of a Coset of $R[x]/\langle f\rangle$ where $f$ is a Polynomial of Degree $d$ in $R[x]$
96071
How to show that a prime ideal of height 2 can’t necessarily be generated by 2 elements? (Hartshorne exercise I.1.11)
93681
Integral closure of $\mathbb{Z}$ in $\mathbb{C}$ is not finitely generated as a $\mathbb{Z}$-module?
118299
Show that $(\mathbb{Z}[x]/(x^{n+1}))^{\times}\cong \mathbb{Z}/2\mathbb{Z}\times\Pi_{i=1}^n\mathbb{Z}$
73743
Number of elements in the quotient ring $\mathbb{Z}[X]/(X^2-3, 2X+4)$
69046
Proof of $\mathbb{Q}$ is not cyclic
32516
show that rational numbers with the multipiciation are not abelian finitely generated group
113216
No field properly between $\mathbb Q$ and $E$ iff $G(K/\mathbb Q) \cong A_4$ or $S_4$