Algebra Defined by Ring Homomorphism is Algebra
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 commutative ring.
Let $\struct {S, +, *}$ be a ring.
Let $f : R \to S$ be a ring homomorphism.
Let the image of $f$ be a subset of the center of $S$.
Let $\struct {S_R, *}$ be the algebra defined by the ring homomorphism $f$.
Then $\struct {S_R, *}$ is an algebra over $R$.
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).