ABSTRACT
Definition 26.1. Let p be a prime. Let S(Z) be the set of all sequences (an) of integers an ∈ Z such that for all n
an ≡ an+1 mod pn. Say that two sequences (an) and (bn) as above are equivalent (write (an) ∼p (bn)) if for all n
an ≡ bn mod pn. Denote by [an] the equivalence class of the sequence (an). Denote by
Zp = S(Z)/ ∼p the set of equivalence classes. Then Zp is a ring with addition and multiplication defined by
[an] + [bn] = [an + bn]
[an][bn] = [anbn].
