Rng homomorphism

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

$𝑓 (𝑎 + 𝑏) = 𝑓 (𝑎) + 𝑓 (𝑏)$
$𝑓 (𝑎 𝑏) = 𝑓 (𝑎) 𝑓 (𝑏)$

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

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Rng homomorphism

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