To prove that an ideal cannot be generated by two elements
3327
Height and minimal number of generators of an ideal
60674
Finitely generated idempotent ideals are principal: proof without using Nakayama's lemma
114640
Showing that an ideal is not a free $R-$module.
81296
If A and B are ideals of a ring, show that A + B = $\{a+b|a \in A, b \in B\}$ is an ideal
21604
A complete ring with respect to an ideal
102341
Primary decomposition of a monomial ideal
95240
Show that $({\mathbb{Q}},+)$ is not finitely generated using the Fundamental Theorem of Finitely Generated Abelian Groups.
151786
Proving that there is no ideal $I$ in $\mathbb{Z}[t]$ such that $\mathbb{Z}[t]/I \cong \mathbb{Q}$
124864
A not free $\mathbb{Z}$-module
137450
Two-sided ideal generated by subset of not commutative ring
112045
A property of minimal prime ideal
11109
The ideal generated by a non-compact operator
18406
An ideal whose radical is maximal is primary
1720
Show that $\langle 2,x \rangle$ is not a principal ideal in $\mathbb Z [x]$
131497
Maximal ideal not containing the set of powers of an element is prime
120181
The ideal generated by $2$ and $ x$ in $\mathbb{Z}[x]$
27167
Ideals in $F[x]$ and Euclidean domains are generated by any element of minimal degree