Ring Homomorphism

A ring homomorphism is a function $f : R \to S$ from a ring $R$ to a ring $S$ that has the following properties, for all $a, b \in R$:

• $f(a + b) = f(a) + f(b)$
• $f(a \cdot b) = f(a) \cdot f(b)$
• $f(1_R) = 1_S$