Université Rennes 1, Année 2013-2014 Master 1 Math., Algèbre

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/6ZA2A3A
2A⊕3A1
A
A A
M A
M{xi}i∈I
M{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∈I
B{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∈I
V A V
A
A
V K
K A A =K
K A A =K
V W K
A V W K
Z Q
1Q
(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.