Definition:Algebra Homomorphism

Definition

Let $R$ be a commutative ring.

Let $\struct {A, *}$ and $\struct {B, \times}$ be algebras over $R$.

An algebra homomorphism $f : A \to B$ is a module homomorphism such that:

$\forall a, b \in A : \map f {a * b} = \map f a \times \map f b$

Also see

• Definition:Unital Algebra Homomorphism

• Results about algebra homomorphisms can be found here.

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