Canonical Basis of Free Module on Set is Basis
Jump to navigation
Jump to search
This theorem requires a proof..
You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof.
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 $R^{(I)}$.
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).