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).

Synonyms: Lie ideal

adjective

1. Optimal; being the best possibility.

2. Perfect, flawless, having no defects.

3. Pertaining to ideas, or to a given idea.