Элементы дискретной математики. Часть I - 143 стр.

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k
K f(x) K[x]
F K F f(x) F
K f(x) K[x]
˜
F
K
˜
F f(x)
˜
F [x]
f(x) K[x]
p(x) f(x)
f(x)=p(x)g(x)
p(x) F
1
K p(x)
α
1
α
1
f(x) F
1
[x]
f(x)=(x α
1
)f
1
(x)
f
1
(x)
n f(x) n =1
˜
F = F
1
n>1 F
1
f
1
(x)
F
2
F
1
K f
1
(x) α
2
F
2
[x]
f(x)=(x α
1
)(x α
2
)f
2
(x)
f
2
(x)
n F
n
K F
n
[x]
f(x)=a(x α
1
)(x α
2
) ...(x α
n
),
a f(x)
p
m
p
p
m p
m
q = p
m
Z
p
p
x
q
x F Z
p
F [x]
x
q
x
F Z
p
b
pb =0 qb =0
H F x
q
x
H = {a |a F & a
q
= a }.