Algebra Defined by Ring Homomorphism is Algebra
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This theorem requires a proof..
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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
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