Anneaux quotient

n
Z/nZ{a, (a, n) = 1}.
Z/9Z
p k >0Z/pkZ
n>1
Z/nZn
Z/nZn
Z/7Z
50 Z/97Z
d n
Z/nZ→Z/dZ
xmod n7→ xmod d
m n
Z/mnZ→Z/mZ×Z/nZ
Z/mnZ→Z/mZ×Z/nZ?
Z/ppcm(m, n)Z
(xmod m, y mod n)x≡ymod pgcd(n, m).
Z(x≡1 [7]
x≡3 [5] ,(x≡1 [45] x≡3 [6] ,(x≡4 [45] x≡1 [6] .
Z/mn Z/n ×Z/m m n
(Z[i],+) Z2
(Z[i],+,·) (Z2,+,·)
A I ⊂A
I
a, b ∈A A a b
{ua +vb, (u, v)∈A2}
A:= C0(R,R)R R
I0:= {f∈A, f(0) = 0}A
I0
A a, b ∈A
a|b⇐⇒ (b)⊂(a).
A I (A
I A/I
I A/I