Let $M$ be a noetherian $R$-module and $I=\mathrm{Ann}_R(M)$. Then $R/I$ is a noetherian ring.
46717
If $M$ is a Noetherian $R$-module, then $R/\text{Ann}(M)$ is a Noetherian ring
158583
Prove that if $M$ is an $R-$ projective left module then $M/IM$ is an $R/I-$ projective left module.
7067
Torsion Modules Annihilators
143884
A non-noetherian ring with noetherian spectrum
74445
Noetherian and Artinian modules
44983
Isomorphism of R-modules
142699
Is $R/N(R)$ a faithfully flat $R$-module?
73235
Rings $R/I \cong h(R)/h(I)\,$ for injective ring hom $h$
49303
In a noetherian integral domain every non invertible element is a product of irreducible elements
50212
$R/Ra$ is an injective module over itself
150911
Prove that the ring is Artinian and find a composition series of ideals
80211
Annihilator of quotient module M/IM
24259
Quotient ring of $T/I$
122189
Show that $M[x]$ is a Noetherian $A[x]$-module.
128493
Given a commutative ring $R$ and an epimorphism of free modules $R^m \to R^n$ is then $m \geq n$?
74974
When $\operatorname{Hom}_{R}(M,N)$ is finitely generated as $\mathbb Z$-module or $R$-module?
23392
The annihilator of a module is an ideal