Added 9 October 2026
ideal
/aɪˈdɪəl/ adjective
Latin root: ideālis Wiktionary
adjective Definition from Wiktionary (CC BY-SA). Pronunciation from Wiktionary, via Kaikki.org. More about ideal at Wordnik → Where our words come from →
- Pertaining to ideas, or to a given idea.
- Existing only in the mind; conceptual, imaginary.
- Optimal; being the best possibility.
noun
- A perfect standard of beauty, intellect etc., or a standard of excellence to aim at.
-
A two-sided ideal; a subset of a ring which is closed under both left and right multiplication by elements of the ring.
Let ℤ be the ring of integers and let 2ℤ be its ideal of even integers. Then the quotient ring ℤ/2ℤ is a Boolean ring.
- A non-empty lower set (of a partially ordered set) which is closed under binary suprema (a.k.a. joins).
Origin
From French idéal, from Late Latin ideālis (“existing in idea”), by surface analysis, idea + -al, from Latin idea (“idea”); see idea. In mathematics, the noun ring theory sense was first introduced by German mathematician Richard Dedekind in his 1871 edition of a text on number theory. The concept was quickly expanded to ring theory and later generalised to order theory. The set theory and Lie theory senses can be regarded as applications of the order theory sense.
From Wiktionary, via Kaikki.org (CC BY-SA)