The Kernel

Let’s consider the residue homomorphism ϕ : Z→ Z4. There are exactly four residue classes modulo 4; namely,

{· · · ,−4, 0, 4, 8, · · ·}, {· · · ,−3, 1, 5, 9, · · ·},

{· · · ,−2, 2, 6, 10, · · ·}, and {· · · ,−1, 3, 7, 11, · · ·}.