最終更新日：2025/12/04
(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.)
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algebra over a field
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元となった辞書の項目
algebra over a field
名詞
(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.)
日本語の意味
体上代数とは、ある体上で定義されたベクトル空間において、ベクトル間の積（すなわち二項演算）が加法およびスカラー倍に対して両線形となる構造を持つものを指す。 / この両線形性により、ベクトル積は分配法則を満たし、その結果、このベクトル空間は環の構造も備える。
意味（1）
(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.)
（ plural ）
