sujets de mémoire. Si l`un d`eux vous tente il vous suffit de m`écrire

R V
R
R
R
V
R=K[x;σ,δ]K V
V
k[x;id.,δ]k
V V
V
V

R R
R r ∈R n(r)∈N∗
rn(r)R
R
R
=⇒=⇒
R[x;σ,δ]
k k < x1, . . . ,xn>
n
D:= k(< x1, . . . ,xn>)D[t]

t−x1, . . . ,t −xn
[t−x1, . . . ,t −xn]ac=cac−1a,c ∈D
[t−x1, . . . ,t −xn]
n= 2 [t−x1,t−x2] = (t−xx2−x1
2)(t−x1) = (t−xx1−x2 1)(t−x2)
xx2−x1
2xx1−x2 1
[t−x1, . . . ,t −xn]
Qn
[t−x1, . . . ,t −xn]
Qn

R K
λ:R−→ K K
λ(R)
P:= ker(λ)K
K RPK
R/P
ker(λ)K
R
λ K
P λ RP
K
R
06=R
A n ×n r < n P,Q n ×r
r×n A =P Q