最終更新日：2025/11/28
(algebra) An integral domain which has a subset whose elements are said to be positive
, such that this subset is closed under addition, closed under multiplication, and all elements of the integral domain satisfy a law of trichotomy; namely, that either that element is in the said subset, or it is the zero (additive identity), or its product with −1 (the additive inverse of the multiplicative identity) belongs to the said subset.
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ordered integral domain
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元となった辞書の項目
ordered integral domain
名詞
(algebra)
An
integral
domain
which
has
a
subset
whose
elements
are
said
to
be
"positive",
such
that
this
subset
is
closed
under
addition,
closed
under
multiplication,
and
all
elements
of
the
integral
domain
satisfy
a
law
of
trichotomy;
namely,
that
either
that
element
is
in
the
said
subset,
or
it
is
the
zero
(additive
identity),
or
its
product
with
−1
(the
additive
inverse
of
the
multiplicative
identity)
belongs
to
the
said
subset.
日本語の意味
整域の一種で、ある部分集合を「正」と指定し、その部分集合が加算および乗算に関して閉じており、また整域の任意の要素について、正であるか、ゼロであるか、またはその加法逆元が正であるかのいずれかの三分法（トリコトミー）が成り立つもの。
意味（1）
(algebra)
An
integral
domain
which
has
a
subset
whose
elements
are
said
to
be
"positive",
such
that
this
subset
is
closed
under
addition,
closed
under
multiplication,
and
all
elements
of
the
integral
domain
satisfy
a
law
of
trichotomy;
namely,
that
either
that
element
is
in
the
said
subset,
or
it
is
the
zero
(additive
identity),
or
its
product
with
−1
(the
additive
inverse
of
the
multiplicative
identity)
belongs
to
the
said
subset.
（ plural ）
