Let $W$ be a submodule of $V$. Prove that if $V/W$ and $W$ are finitely generated then so is $V$.
9806
$M$ finitely generated if submodule and quotient are finitely generated.
114267
If $S$ is a finitely generated graded algebra over $S_0$, $S_{(f)}$ is finitely generated algebra over $S_0$?
69141
Is every Noetherian module finitely generated?
100303
A necessary and sufficient condition for $A\cap(B+C)=(A\cap B)+C$ to hold for submodules
50114
A question about direct sums and products of modules
157585
Structure theorem of finite rings
86034
Is it true that for algebraic sets $V,W$ we have $I(V \times W ) =I(V) + I(W)$?
53364
dim$(V)$ = $n$, dim$(W)$ = $m$ $\implies$ dim($L(V,W)$) = $nm$
103349
A question about a proof of Noetherian modules and exact sequences
104578
Suppose that $V$ is a vector space, and $W$ is a subspace of $V$. If $V$ is finite dimensional, then prove $W$ too must be finite dimensional.
15300
How to show that $(W^\bot)^\bot=W$ (in a finite dimensional vector space)
95930
Finitely generated modules over a Noetherian ring are Noetherian
54380
Prove if $|z| < 1$ and $ |w| < 1$, then $|1-zw^*| \neq 0$ and $| {{z-w} \over {1-zw^*}}| < 1$
59687
Suppose $M$ is a finitely generated module over $R$ where $R$ is a Noetherian ring. Prove that $M$ is a noetherian module.
128861
If $M$ isn't Noetherian, $M$ has a submodule maximal with respect to being not finitely generated.
42652
Must $k$-subalgebra of $k[x]$ be finitely generated?
34065
Submodule of free module over a p.i.d. is free even when the module is not finitely generated?