[[Rng]]
# Rng homomorphism

A **rng homomorphism** is a [[Morphism|morphism]] in [[Category of rngs]], 
that is to say a structure-preserving map between [[rng|rngs]]. #m/def/ring 
Let $A,B$ be rngs and let $f : A \to B$.
Then $f$ is a homomorphism iff for any $x,y \in A$

1. $f(a + b) = f(a) + f(b)$
2. $f(ab)=f(a)f(b)$

that is to say $f$ is a [[group homomorphism|homomorphism]] of both the additive group and the multiplicative monoid.
For unital rings, see [[Ring homomorphism]].

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#state/tidy | #lang/en | #SemBr