If $M$ is finitely generated left module over a left noetherian ring $R$, then $M$ is a noetherian module.
95930
Finitely generated modules over a Noetherian ring are Noetherian
116955
Showing the existence of a certain kind of extension of a finitely generated algebra
93670
A surjective endomorphism (of a Noetherian ring) is injective.
74314
Noetherian ring and the same prime divisors
80302
A module $M$ whose submodules and factor modules are semisimple but not semisimple itself
117211
Infinite linear independent family in a finitely generated $A$-module
104747
Does localisation commute with Hom for finitely-generated modules?
124864
A not free $\mathbb{Z}$-module
77382
Left ideals of $M_n(K)$
47086
Quotient rings and free modules
44396
Noetherian Ring under a Homomorphism / homomorphic function / map
145758
Are submodules of finitely generated free modules always free?
9562
Proving that surjective endomorphisms of Noetherian modules are isomorphisms and a semi-simple and noetherian module is artinian.
157585
Structure theorem of finite rings
16643
A slick proof that a field which is finitely generated as a ring is finite
145722
Prove there is a bijection between the set of $R[x]$-module structures on $M$ and $\mathrm{End}_{R-\mathsf{Mod}}(M)$.
33063
Are all simple left modules over a simple left artinian ring isomorphic?