If $M/N$ and $N$ are noetherian $R$-modules then so is $M$
7645
Noetherian property for exact sequence
76813
The ring $ℤ/nℤ$ is a field if and only if $n$ is prime
74974
When $\operatorname{Hom}_{R}(M,N)$ is finitely generated as $\mathbb Z$-module or $R$-module?
102072
Simple $M_n(D)$-module with $D$ a division ring
60804
About the property of $m$: if $n < m$ is co-prime to $m$, then $n$ is prime
29231
Proof of : $x^{n}\equiv x^{\varphi(m)+[n \bmod \varphi(m)]} \mod m$
62227
Is a product of two Noetherian schemes over Spec $\mathbb Z$ a Noetherian scheme?
67706
If $R$ is a Noetherian ring then $R[[x]]$ is also Noetherian
128861
If $M$ isn't Noetherian, $M$ has a submodule maximal with respect to being not finitely generated.
26805
Non-Noetherian 0-dimensional ring
83812
Artinian ring and faithful module of finite length
147157
Modules over commutative rings
87151
Primary ideals in Noetherian rings
150986
For a Noetherian ring $R$, we have $\text{Ass}_R(S^{-1}M)=\text{Ass}_R(M)\cap \{P:P\cap S=\emptyset\}$
66866
Algebraic dual of $\mathbb{R}^{\mathbb{N}}$
138058
Prove that $\mathbb Z_{m}\times\mathbb Z_{n} \cong \mathbb Z_{mn}$ implies $\gcd(m,n)=1$.
68167
Intersection of powers of an ideal in a Noetherian ring