A perfect standard of beauty, intellect etc., or a standard of excellence to aim at.
A subring closed under multiplication by its containing ring.
(lattice theory) 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.
(Lie theory) A Lie subalgebra (subspace that is closed under the Lie bracket) ???? of a given Lie algebra ???? such that the Lie bracket [????,????] is a subset of ????.
Optimal; being the best possibility.
Perfect, flawless, having no defects.
Pertaining to ideas, or to a given idea.
Existing only in the mind; conceptual, imaginary.
Teaching or relating to the doctrine of idealism. Example: the ideal theory or philosophy
Not actually present, but considered as present when limits at infinity are included. Example: An ideal triangle in the hyperbolic disk is one bounded by three geodesics that meet precisely on the circle.
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