A perfect standard of beauty, intellect etc., or a standard of excellence to aim at. / (algebra, ring theory) A subring closed under multiplication by its containing ring.

(philosophy) An abstract archetype of a given thing, compared to which real-life examples are seen as imperfect approximations; pure essence, as opposed to actual examples.

(transitive) To establish the identity of someone or something. / (transitive) To disclose the identity of someone. / (transitive, biology) To establish the taxonomic classification of an organism.

(strictly) The act of identifying (i.e., which one, which thing).

(algebra) An element of an algebraic structure, generally denoted 1, which is an identity for a multiplicative operation (generally denoted × or *, or by concatenation).

(algebra) An element of an algebraic structure, generally denoted 0, which is an identity for an additive operation (generally denoted +). That is, x + 0 = 0 + x = x for any x in the structure.

Sameness, identicalness; the quality or fact of (several specified things) being the same.

Doctrine, philosophy, body of beliefs or principles belonging to an individual or group. / (uncountable) The study of the origin and nature of ideas.

(algebra) An element of a structure that produces an identity mapping when applied on the right.

(algebra) An element of a structure that produces an identity mapping when applied on the left.