S erie 2

2Z⊂Z(X)⊂Z[X] (2,1 + √−5) ⊂Z[√−5]
0⊂Z(X)⊂Z[X] (2,1 + √−5) ⊂Z[√−5]
I J
I·J=I∩J I ∪J I ∩J
3
2Z⊂Z1+√−3 2O
KK=Q(√−3) 1+√2
2O
KK=Q(√2,√7)
K=Q(i)O
K=Z[i] NK:Q(α) = N(α)>0
α∈K
βZ[i]β1+2i2−3i
α, β ∈Z[i] N(α)>N(β)γ δ
O
K
α=γ·β+δ
N(δ)<N(β)α γ ·β
« » βZ[i]
Z[i]
1−i α 2 = α·(1−i)2
5 = (2 + i)·(2 −i) = (1 + 2i)·(1 −2i)
Z[i]
54 = 2 ·33=13 + √−47
2·13 −√−47 2
K=Q(√−47)
d p 2d
K=Q(√d)pO
K
(d
p) = −1
AZ[√−3] I A 2 1 + √−3
2A6=I I2= 2A·I I
A

K I O
KN(I)
NK:Q(α)α∈I
I K N(I)
I