ordered integral domain

noun

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.

Ask AI about this wordChatGPTClaudePerplexityGoogle AIGrok

Meanings

nounordered integral domain (plural ordered integral domains)

plural ordered integral domains

  1. algebraAn 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.
Cite this entry
APA

ordered integral domain. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/ordered%20integral%20domain

MLA

“ordered integral domain.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/ordered%20integral%20domain. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. “ordered integral domain,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/ordered%20integral%20domain.

Source: ordered integral domain on Wiktionary, CC BY-SA 4.0.