$M + N$ and $M \cap N$ are finitely generated $A$-modules implies $M$ and $N$ finitely generated using exact sequences
14259
If M+N and M$\cap$N are finitely generated modules, so are M and N.
66866
Algebraic dual of $\mathbb{R}^{\mathbb{N}}$
101095
Constructing an example s.t. $\operatorname{Hom}_R(M,N)$ is not finitely generated
28136
$A^m\hookrightarrow A^n$ implies $m\leq n$ for a ring $A\neq 0$
124151
Finite ring extension and number of maximal ideals
92211
When are $\mathbb Z_m$ and $\mathbb Z_n$ homomorphic?
63541
Projective and injective modules; direct sums and products
155266
Is $\exp:\overline{\mathbb{M}}_n\to\mathbb{M}_n$ injective?
60674
Finitely generated idempotent ideals are principal: proof without using Nakayama's lemma
140938
Finitely generated projective module
76047
Annihilators of elements of a finitely generated faithful module over a noetherian reduced ring
128861
If $M$ isn't Noetherian, $M$ has a submodule maximal with respect to being not finitely generated.
158583
Prove that if $M$ is an $R-$ projective left module then $M/IM$ is an $R/I-$ projective left module.
79591
Exact Sequences of Modules and Rank
141900
Exact sequence and Noetherian modules
587
Ideal Generated by the Union of Two Ideals
83812
Artinian ring and faithful module of finite length