Definition:Zero Homomorphism

Definition
Let $\struct {R_1, +_1, \circ_1}$ and $\struct {R_2, +_2, \circ_2}$ be rings with zeroes $0_1$ and $0_2$ respectively.

Consider the mapping $\zeta: R_1 \to R_2$ defined as:
 * $\forall r \in R_1: \map \zeta r = 0_2$

Then $\zeta$ is the zero homomorphism from $R_1$ to $R_2$.

Also known as
The zero homomorphism is also referred to by some authors as the trivial homomorphism.

Also see

 * Constant Mapping to Identity is Homomorphism: $\zeta$ is indeed a (ring) homomorphism.