Examples of modules such that $M\oplus N_1\simeq M\oplus N_2$, but $N_1\not\simeq N_2$?
105233
Is there a counterexample for the claim: if $A \oplus B\cong A\oplus C$ then $B\cong C$?
101095
Constructing an example s.t. $\operatorname{Hom}_R(M,N)$ is not finitely generated
47630
Endomorphisms of modules satisfying chain conditions and counterexamples.
117211
Infinite linear independent family in a finitely generated $A$-module
141149
Proof some module is direct sum by its submodules.
85799
Finding languages such that $L_{1} \subseteq L_{2} \subseteq L_{3}$ where $L_{1}, L_{3} \notin \mathbb{R}$, $L_{2} \in \mathbb{R}$
37570
$M + N$ and $M \cap N$ are finitely generated $A$-modules implies $M$ and $N$ finitely generated using exact sequences
37479
Proper submodules of Noetherian modules are intersections of indecomposable modules
36142
What is $\mathbb Z \oplus \mathbb Z / \langle (2,2) \rangle$ isomorphic to?
86015
$\mathbb Q[x]/(x^2+1)$ is not isomorphic to $\mathbb Q[x]/(x^2+2)$
26244
Pathologies in module theory
7870
For $M\otimes_R N$, why is it so imperative that $M$ be a right $R$-module and $N$ a left $R$-module?
70872
Isomorphism of quotient modules implies isomorphism of submodules?
100303
A necessary and sufficient condition for $A\cap(B+C)=(A\cap B)+C$ to hold for submodules
45627
Find a sub-ring of M(2, $\mathbb{Q}$) which is isomorphic to $\mathbb{Q}$
45179
When does the isomorphism $G\simeq \ker(\phi)\times \operatorname{im}(\phi)$? hold?
9806
$M$ finitely generated if submodule and quotient are finitely generated.