Dimension

(Pi)i∈NK[X]A[X]
deg Pi=i i ∈N(Pi)K[X]A[X]
E K (Fi)i∈I
E J K I
∩i∈IFi=∩j∈JFjPi∈IFi=Pk∈KFk
E A (ei)i∈IE A(I)
E∗E A
E∗AI
K(x1,· · · , xn)∈Kn
(α1,· · · , αn)∈KnP∈Kn−1[X]P(xi) = αi1≤i≤n
KZ
K⊂K0E K0
E K0K0K E
KdimKE= dimKK0·dimK0E E
K K0E6={0}K0
K
R C K
p n ∈N#K=pn
(a, b)∈Z2Z
Z2(c, d)(2,3); (c, d)Z2
E F K n p f ∈ L(E, F )
r A L(F, E)A={g∈ L(F, E)/f ◦g◦f=
0}
E K f ∈ L(E)
P∈K[X]P(f) = 0
fR8rgf2= 4 f
x0=−∞ xn+1 = +∞x1<· · · < xn
C1R]xi, xi+1[
2
p F pnE F
n
E
K L α ∈L K
P∈K[X]P(α) = 0 α K K[α]
K[α]K
L K