![abstract algebra - How to prove that as an $R$-module, $\mathbb{C}^n$ is finitely generated iff $R=\mathbb{C}[x]$. - Mathematics Stack Exchange abstract algebra - How to prove that as an $R$-module, $\mathbb{C}^n$ is finitely generated iff $R=\mathbb{C}[x]$. - Mathematics Stack Exchange](https://i.stack.imgur.com/xxHJE.png)
abstract algebra - How to prove that as an $R$-module, $\mathbb{C}^n$ is finitely generated iff $R=\mathbb{C}[x]$. - Mathematics Stack Exchange
![abstract algebra - Basis of a subset of finitely generated torsion-free module - Mathematics Stack Exchange abstract algebra - Basis of a subset of finitely generated torsion-free module - Mathematics Stack Exchange](https://i.stack.imgur.com/khETv.png)
abstract algebra - Basis of a subset of finitely generated torsion-free module - Mathematics Stack Exchange
![commutative algebra - Every submodule is finitely generated iff every nonempty collection of submodules has a maximal element - Mathematics Stack Exchange commutative algebra - Every submodule is finitely generated iff every nonempty collection of submodules has a maximal element - Mathematics Stack Exchange](https://i.stack.imgur.com/kqZEh.png)
commutative algebra - Every submodule is finitely generated iff every nonempty collection of submodules has a maximal element - Mathematics Stack Exchange
![abstract algebra - Let $M$ be a free module over a PID with finite rank, then any submodule $N \subset M$ is also free with finite rank - Mathematics Stack Exchange abstract algebra - Let $M$ be a free module over a PID with finite rank, then any submodule $N \subset M$ is also free with finite rank - Mathematics Stack Exchange](https://i.stack.imgur.com/XV1sd.png)
abstract algebra - Let $M$ be a free module over a PID with finite rank, then any submodule $N \subset M$ is also free with finite rank - Mathematics Stack Exchange
![principal ideal domains - Need help understanding a step in a proof about modules over PIDs - Mathematics Stack Exchange principal ideal domains - Need help understanding a step in a proof about modules over PIDs - Mathematics Stack Exchange](https://i.stack.imgur.com/T1IdY.png)
principal ideal domains - Need help understanding a step in a proof about modules over PIDs - Mathematics Stack Exchange
![Sub-module | Finitely generated module| cyclic module | Advanced abstract algebra full lectures - YouTube Sub-module | Finitely generated module| cyclic module | Advanced abstract algebra full lectures - YouTube](https://i.ytimg.com/vi/lQPWWr5sCwc/mqdefault.jpg)