Feuille d`exercices 3

Q Z/nZ
n∈N Z Q Z/nZ
Z Z/nZ Q
M A N M N M/N
M M N
M/N
A
A
Z ZN
A=Z/6ZA2A3A2A⊕3A
1
A A
A
M A M
{xi}i∈IM{rj}j∈J
A(I)→M ei7→ xiA=Z[X]
A I = (2, X)⊂A
A A
A
Z/2Z Z Z
B A B
{xi}i∈IB{yj}j∈J
A[Xi]i∈I→B Xi7→ xiA k
k X k
1

A M
A M n ∈NM
An
A
M A M
AZNM:= A A
N:= Z(N)A
M A N M N M/N
M
A K A
K K A
V K (vi)i∈IV
A V A
A V K
K A A =K
K A A =K
V W K A V
W K
Z Q 1
Q
(ei)i∈IZ Q j∈I(ei)i∈I\{j}
N A M π :M−→ M/N
P7−→ π−1(P)M/N
M N
N⊂L⊂M(M/N)/(L/N)'M/L
P M N/(N∩P)'(N+P)/P