最終更新日:2024/08/06
(algebra, Galois theory) (of a polynomial) Given a polynomial p over a field K, the smallest extension field L of K such that p, as a polynomial over L, decomposes into linear factors (polynomials of degree 1); (of a set of polynomials) given a set P of polynomials over K, the smallest extension field of K over which every polynomial in P decomposes into linear factors.
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splitting field
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元となった辞書の項目
splitting field
noun
(algebra,
Galois
theory)
(of
a
polynomial)
Given
a
polynomial
p
over
a
field
K,
the
smallest
extension
field
L
of
K
such
that
p,
as
a
polynomial
over
L,
decomposes
into
linear
factors
(polynomials
of
degree
1);
(of
a
set
of
polynomials)
given
a
set
P
of
polynomials
over
K,
the
smallest
extension
field
of
K
over
which
every
polynomial
in
P
decomposes
into
linear
factors.
意味(1)
(algebra,
Galois
theory)
(of
a
polynomial)
Given
a
polynomial
p
over
a
field
K,
the
smallest
extension
field
L
of
K
such
that
p,
as
a
polynomial
over
L,
decomposes
into
linear
factors
(polynomials
of
degree
1);
(of
a
set
of
polynomials)
given
a
set
P
of
polynomials
over
K,
the
smallest
extension
field
of
K
over
which
every
polynomial
in
P
decomposes
into
linear
factors.
意味(2)
意味(3)