Let $A \subset B \subset C$ be subrings. If $C$ is finitely generated as an $A$-module, is $B$ finitely generated as an $A$-module?
107207
$A\subseteq B\subseteq C$ ring extensions, $A\subseteq C$ finite/finitely-generated $\Rightarrow$ $A\subseteq B$ finite/finitely-generated?
95930
Finitely generated modules over a Noetherian ring are Noetherian
141100
Nontrivial subring with unity different from the whole ring?
109682
Proposed proof of: If $A \subset B \subset \bar{A}$ and $A$ is connected, then $B$ is connected
115541
Subrings of polynomial rings over the complex plane
124864
A not free $\mathbb{Z}$-module
26368
Finitely generated graded modules over $K[x]$
69141
Is every Noetherian module finitely generated?
141149
Proof some module is direct sum by its submodules.
2719
Why isn't an infinite direct product of copies of $\Bbb Z$ a free module?
114267
If $S$ is a finitely generated graded algebra over $S_0$, $S_{(f)}$ is finitely generated algebra over $S_0$?
100303
A necessary and sufficient condition for $A\cap(B+C)=(A\cap B)+C$ to hold for submodules
36631
Is $[0,1] \cap \Bbb Q$ a compact subset of $\Bbb Q$?
103349
A question about a proof of Noetherian modules and exact sequences
29635
Fields finitely generated as $\mathbb Z$-algebras are finite?
29626
Is there a proper subfield $K\subset \mathbb R$ such that $[\mathbb R:K]$ is finite?
20335
If $A\subset B$ then $\bar{A}\subset \bar{B}$