ABSTRACT
In practice when we think of the ring Z4 we think of the four elements [0], [1], [2], [3] (or even 0, 1, 2, 3) together with the appropriate operations. But technically, when we first considered Z4 and its operations in Chapter 3, we defined those elements as infinite sets of integers; that is,
[a] = {a+ 4m : m ∈ Z} = {n ∈ Z : 4|(a− n)}. We then defined addition and multiplication by setting
[a] + [b] = [a+ b] and [a][b] = [ab].
