# 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

From ProofWiki

Jump to: navigation, search

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.

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).*

- This page was last modified on 29 July 2017, at 05:12 and is 587 bytes
- Content is available under Creative Commons Attribution-ShareAlike License unless otherwise noted.