Definition:Algebra Defined by Ring Homomorphism
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Definition
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 $S_R$ be the module defined by the ring homomorphism $f$.
The algebra defined by $f$ is the algebra over $R$ defined as:
- $\struct {S_R, *}$
Also see
Properties
- Algebra Defined by Ring Homomorphism is Associative
- Algebra Defined by Ring Homomorphism on Ring with Unity is Unitary
- Algebra Defined by Ring Homomorphism on Commutative Ring is Commutative
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