A perfect standard of beauty, intellect etc., or a standard of excellence to aim at.
A subsemigroup with the property that if any semigroup element outside of it is added to any one of its members, the result must lie outside of it.
A subring closed under multiplication by its containing 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.
A Lie subalgebra (subspace that is closed under the Lie bracket) 𝖍 of a given Lie algebra 𝖌 such that the Lie bracket [𝖌,𝖍] is a subset of 𝖍.
Not actually present, but considered as present when limits at infinity are included.
Optimal; being the best possibility.
Existing only in the mind; conceptual, imaginary.
Pertaining to ideas, or to a given idea.
Perfect, flawless, having no defects.
Teaching or relating to the doctrine of idealism.
An inherently advantageous or excellent quality of something or someone; a favourable point, an advantage.
A creature embodying divine power, specifically one of the orders of heavenly beings, traditionally ranked above angels and below archangels.
Accordance with moral principles; conformity of behaviour or thought with the strictures of morality; good moral conduct.
A particular manifestation of moral excellence in a person; an admirable quality.
Specifically, each of several qualities held to be particularly important, including the four cardinal virtues, the three theological virtues, or the seven virtues opposed to the seven deadly sins.
Specifically, moral conduct in sexual behaviour, especially of women; chastity.
The inherent power or efficacy of something (now only in phrases).