Semiring Homomorphism

A function $f:R\to S$ between Semirings is a semiring homomorphism if

• $f(0)=0$
• $f(x+y)=f(x)+f(y)$
• $f(1)=1$
• $f(x\cdot y)=f(x)\cdot f(y)$

Note that unlike Ring Homomorphisms, we must include the condition that $f(0)=0$, as units are Property-Like Structure in Monoids.