ordered integral domain

Noun

 * 1)  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 &minus;1 (the additive inverse of the multiplicative identity) belongs to the said subset.