IDEAL

noun

1. A perfect standard of beauty, intellect etc., or a standard of excellence to aim at.
2. A subring closed under multiplication by its containing ring.
3. (lattice theory) A non-empty lower set (of a partially ordered set) which is closed under binary suprema (a.k.a. joins).

adjective

1. Optimal; being the best possibility.
2. Perfect, flawless, having no defects.
3. Pertaining to ideas, or to a given idea.