Unnumbered source etymology
Original entry ↗Pertaining to ideas, or to a given idea. · Existing only in the mind; conceptual, imaginary. · Optimal; being the best possibility. · Perfect, flawless, having no defects.
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. · A non-empty lower set (of a partially ordered set) which is closed under binary suprema (a.k.a. joins). · A collection of sets, considered small or negligible, such that every subset of each member and the union of any two members are also members of the collection.
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.
Relationships mentioned by the source
These are extracted mentions, not a timeline or a verified sequence of immediate parents.
This page abbreviates 4 auxiliary source items. The etymology narrative is not shortened. Omission counts are available in the audit fields below; consult the original for complete auxiliary material.
Inspect preserved source fields
Raw extraction fields are retained for auditing. Their order does not establish ancestry.
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