Last Updated：2025/11/19
(algebra) An algebraic structure which consists of a set with two binary operations: an additive operation and a multiplicative operation, such that the set is an abelian group under the additive operation, a monoid under the multiplicative operation, and such that the multiplicative operation is distributive with respect to the additive operation.
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IPA(Pronunciation)
Noun
(algebra)
An
algebraic
structure
which
consists
of
a
set
with
two
binary
operations:
an
additive
operation
and
a
multiplicative
operation,
such
that
the
set
is
an
abelian
group
under
the
additive
operation,
a
monoid
under
the
multiplicative
operation,
and
such
that
the
multiplicative
operation
is
distributive
with
respect
to
the
additive
operation.
Japanese Meaning
環（かん）：代数学における代数的構造の一種。集合に対して二つの二項演算（加法と乗法）が定義され、加法についてはアーベル群となり、乗法についてはモノイドあるいは半群の構造を持ち、乗法が加法に分配される性質を持つ。
Sense（1）
(algebra)
An
algebraic
structure
which
consists
of
a
set
with
two
binary
operations:
an
additive
operation
and
a
multiplicative
operation,
such
that
the
set
is
an
abelian
group
under
the
additive
operation,
a
monoid
under
the
multiplicative
operation,
and
such
that
the
multiplicative
operation
is
distributive
with
respect
to
the
additive
operation.
（ plural ）
