1. Racines d`un polynôme 2. Exercice 3. Idéaux premiers et

P=X5+ 2X3−24X−2
PZ[X]
x1,···, x5P N2=x2
1+x2 2+x2 3+x2 4+x2 5
P
P P (−1) P(0)
K K[X, Y ]
A x A n ≥1xn= 0
x A
A
x∈A I
xn, n ≥1
I
A A
I A x, y ∈A xy ∈I n ≥1
xn∈I yn∈I
Z
I A I √I x ∈A
n∈Nxn∈I
I A √I=p√I
A K
A[X]A[X]K[X]
A A[X]
K[X]
A0=R[X, Y ]/(Y2−X3)A0[P]
P
K0A0P(T) = T2−[X]∈A0[T]P
A0[T]K0[T]
A0