最終更新日：2024/08/06
(algebra) A module (over some ring) with an additional binary operation, a module-element-valued product between module elements, which is bilinear over module addition and scalar multiplication. (N.B.: such bilinearity implies distributivity of the module multiplication with respect to the module addition, which means that such a module is also a ring.)
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algebra over a ring
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元となった辞書の項目
algebra over a ring
noun
(algebra)
A
module
(over
some
ring)
with
an
additional
binary
operation,
a
module-element-valued
product
between
module
elements,
which
is
bilinear
over
module
addition
and
scalar
multiplication.
(N.B.:
such
bilinearity
implies
distributivity
of
the
module
multiplication
with
respect
to
the
module
addition,
which
means
that
such
a
module
is
also
a
ring.)
意味（1）
(algebra)
A
module
(over
some
ring)
with
an
additional
binary
operation,
a
module-element-valued
product
between
module
elements,
which
is
bilinear
over
module
addition
and
scalar
multiplication.
(N.B.:
such
bilinearity
implies
distributivity
of
the
module
multiplication
with
respect
to
the
module
addition,
which
means
that
such
a
module
is
also
a
ring.)
