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検索内容:
perfect field
noun
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.
field ice
algebra over a field
noun
(algebra)
A
vector
space
(over
some
field)
with
an
additional
binary
operation,
a
vector-valued
product
between
vectors,
which
is
bilinear
over
vector
addition
and
scalar
multiplication.
(N.B.:
such
bilinearity
implies
distributivity
of
the
vector
multiplication
with
respect
to
the
vector
addition,
which
means
that
such
a
vector
space
is
also
a
ring.)
gas field
noun
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