Definitions from Wiktionary ( )

▸ adjective:  Pertaining to ideas, or to a given idea.
▸ adjective:  Existing only in the mind; conceptual, imaginary.
▸ adjective:  Optimal; being the best possibility.
▸ adjective:  Perfect, flawless, having no defects.
▸ adjective:  Teaching or relating to the doctrine of idealism.
▸ adjective:  (mathematics) Not actually present, but considered as present when limits at infinity are included.
▸ noun:  A thing which exists in the mind but not in reality; in ontological terms, a thing which has essence but not existence.
▸ noun:  A perfect standard of beauty, intellect etc., or a standard of excellence to aim at.
▸ noun:  (algebra, ring theory) A subring closed under multiplication by its containing ring.
▸ noun:  (algebra, order theory, lattice theory) A non-empty lower set (of a partially ordered set) which is closed under binary suprema (a.k.a. joins).
▸ noun:  (set theory) 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.
▸ noun:  (algebra, Lie theory) 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.
▸ noun:  (algebra) 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.
▸ noun:  A city in Georgia, United States.
▸ noun:  An unincorporated community in Illinois.
▸ noun:  An unincorporated community in South Dakota.

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