English Dictionary

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。

In my abstract algebra course we proved that every ordered integral domain can be embedded into a field that preserves the order.

私の抽象代数学の授業では、正の元の集合が加法と乗法で閉じ、三分法を満たす順序を備えた整域（順序整域）が、その順序を保つ体に埋め込めることを証明しました。

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.

ordered integral domains （ plural ）