# Canonical Basis of Free Module on Set is Basis

## Theorem

Let $R$ be a ring with unity.

Let $I$ be a set.

Let $R^{(I)}$ be the free $R$-module on $I$.

Let $B$ be its canonical basis.

Then $B$ is a basis of $R^{(I)}$.

From ProofWiki

Jump to: navigation, search

Let $R$ be a ring with unity.

Let $I$ be a set.

Let $R^{(I)}$ be the free $R$-module on $I$.

Let $B$ be its canonical basis.

Then $B$ is a basis of $R^{(I)}$.

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 08:24 and is 404 bytes
- Content is available under Creative Commons Attribution-ShareAlike License unless otherwise noted.