ideal vs kernel

ideal

noun
  • 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. 

  • 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. 

  • A subring closed under multiplication by its containing ring. 

  • A non-empty lower set (of a partially ordered set) which is closed under binary suprema (a.k.a. joins). 

  • A perfect standard of beauty, intellect etc., or a standard of excellence to aim at. 

  • 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. 

adj
  • Not actually present, but considered as present when limits at infinity are included. 

  • Optimal; being the best possibility. 

  • Existing only in the mind; conceptual, imaginary. 

  • Pertaining to ideas, or to a given idea. 

  • Perfect, flawless, having no defects. 

  • Teaching or relating to the doctrine of idealism. 

kernel

noun
  • The set of members of a fuzzy set that are fully included (i.e., whose grade of membership is 1). 

  • The human clitoris. 

  • The nucleus and electrons of an atom excluding its valence electrons. 

  • For a category with zero morphisms: the equalizer of a given morphism and the zero morphism which is parallel to that given morphism. 

  • A set of pairs of a mapping's domain which are mapped to the same value. 

  • A single seed or grain, especially of corn or wheat. 

  • A small mass around which other matter is concreted; a nucleus; a concretion or hard lump in the flesh. 

  • The core, center, or essence of an object or system. 

  • The central part of many computer operating systems which manages the system's resources and the communication between hardware and software components. 

  • The stone of certain fruits, such as peaches or plums. 

  • A function used to define an integral transform. 

  • The core engine of any complex software system. 

  • The central (usually edible) part of a nut, especially once the hard shell has been removed. 

  • For a given function (especially a linear map between vector spaces), the set of elements in the domain which are mapped to zero; (formally) given f : X → Y, the set {x ∈ X : f(x) = 0}. 

verb
  • To enclose within a kernel 

  • To crenellate 

How often have the words ideal and kernel occurred in a corpus of books? (source: Google Ngram Viewer )