Existence of submodules
134294
A (not necessarily unitary) $R$ module $M$ splits into $B\oplus C$ where $B$ is unitary and $RC=\{0\}$.
156178
Do counit-unit adjunctions have the expected universal properties?
73662
Example of non-flat modules
63541
Projective and injective modules; direct sums and products
37479
Proper submodules of Noetherian modules are intersections of indecomposable modules
145722
Prove there is a bijection between the set of $R[x]$-module structures on $M$ and $\mathrm{End}_{R-\mathsf{Mod}}(M)$.
116955
Showing the existence of a certain kind of extension of a finitely generated algebra
59446
Universal property of universal bundles.
68753
Elements in finite field extensions
121246
Projective modules and $\hom(P,\cdot)$
42652
Must $k$-subalgebra of $k[x]$ be finitely generated?
40087
Using Modularity Theorem and Ribet's Theorem to disprove existence of rational solutions
58803
${n \choose k} \bmod m$ using Chinese remainder theorem?
18329
How do I remove a submodule?
120637
Is there a unique cyclic submodule for every factor dividing the order of a cyclic module?
9806
$M$ finitely generated if submodule and quotient are finitely generated.
102938
$\Bbb F_2[X]$ modules with 8 elements