Bases of Finitely Generated Free Module have Equal Cardinality
Theorem
Let $R$ be a commutative ring with unity.
Let $M$ be finitely generated.
Let $B$ and $C$ be bases of $M$.
Then $B$ and $C$ are finite and have the same cardinality.
Proof
You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof.
When this page/section has been completed, {{ProofWanted}} should be removed from the code.
If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page (see the proofread template for usage).
