Série 8

Z/180Z
Z[t]
hti,h42i,h89i,ht+t9i.
f∈Z[x]f
f1−1
f, g ∈Z[x]f g Q[x]
f g Z[x]
f∈Z[x]
Q[x]
p > 1p
(p−1)! ≡ −1 mod p.
p∈Np≡1 mod 4
x∈Zx2≡ −1 mod p
x= 1 ·2·3·. . . ·p−1
2
Z[i]/(p)∼
=Fp[t]/(t2+ 1)
pZ[i]
p
deg : Z[i]− {0} → N

R=Z√−5
3∈R
R
R=Z[i]
2∈R
R
K
a∈K(x−a)K[x]
f∈K[x]K[x] (x−a)f
b∈K(x−b)K[x, y]