Rng homomorphism

A rng homomorphism is a morphism in $𝖱 𝗇 𝗀$ , that is to say a structure-preserving map between rngs. #m/def/ring Let $𝐴, 𝐵$ be rngs and let $𝑓 : 𝐴 \to 𝐵$ . Then $𝑓$ is a homomorphism iff for any $𝑥, 𝑦 \in 𝐴$

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

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

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