Every non-Noetherian module has a submodule maximal with respect to being not finitely generated.
128861
If $M$ isn't Noetherian, $M$ has a submodule maximal with respect to being not finitely generated.
37479
Proper submodules of Noetherian modules are intersections of indecomposable modules
131497
Maximal ideal not containing the set of powers of an element is prime
130466
Proving every prime ideal is maximal in a finite dimensional ring over a field.
149753
The structure of a Noetherian ring in which every element is an idempotent.
68202
Must an ideal generated by an irreducible element be a maximal ideal?
96144
Every element outside the maximal ideal of a local ring is a unit
124151
Finite ring extension and number of maximal ideals
6307
maximal ideal not containing some expression
114773
counterexamples on modules
107002
Noetherian ring whose ideals have arbitrarily large number of generators
122012
The ideal $(x,y)$ is not a free $K[x,y]$-module
63338
Noncommutative failure of IBN: $\,R^n\cong R^m \Rightarrow n - m,$ ring $R$ with maximal ideal $I$ such that $R/I$ is not a division ring?
70712
How to prove that $k[x, xy, xy^2, \dotsc]$ is not noetherian?
17991
Nonconstant polynomials do not generate maximal ideals in $\mathbb Z[x]$
122189
Show that $M[x]$ is a Noetherian $A[x]$-module.
139794
In a (not necessarily commutative) ring, a nilpotent maximal ideal is unique.