Synsets for "ideal"
Synset: ideal.n.01
Synonyms: ideal
Part of Speech: NOUN
Definition: the idea of something that is perfect; something that one hopes to attain
Examples:
Lemmas: ideal
Hypernym: idea
Hyponym: criterion ego_ideal exemplar paragon value
Antonyms:
Synset: ideal.n.02
Synonyms: ideal
Part of Speech: NOUN
Definition: model of excellence or perfection of a kind; one having no equal
Examples:
Lemmas: ideal paragon nonpareil saint apotheosis nonesuch nonsuch
Hypernym: model
Hyponym: class_act humdinger jimdandy
Antonyms:
Synset: ideal.s.01
Synonyms: ideal
Part of Speech: ADJECTIVE SATELLITE
Definition: conforming to an ultimate standard of perfection or excellence; embodying an ideal
Examples:
Lemmas: ideal
Hypernym:
Hyponym:
Antonyms:
Synset: ideal.s.02
Synonyms: ideal
Part of Speech: ADJECTIVE SATELLITE
Definition: constituting or existing only in the form of an idea or mental image or conception
Examples: a poem or essay may be typical of its period in idea or ideal content
Lemmas: ideal
Hypernym:
Hyponym:
Antonyms:
Synset: ideal.a.03
Synonyms: ideal
Part of Speech: ADJECTIVE
Definition: of or relating to the philosophical doctrine of the reality of ideas
Examples:
Lemmas: ideal idealistic
Hypernym:
Hyponym:
Antonyms:
Related Wikipedia Samples:
Article | Related Text |
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Irreducible ideal | Every prime ideal is irreducible. Every irreducible ideal of a Noetherian ring is a primary ideal, and consequently for Noetherian rings an irreducible decomposition is a primary decomposition. Every primary ideal of a principal ideal domain is an irreducible ideal. Every irreducible ideal is a primal ideal. |
Radical of an ideal | If "I" is an ideal, formula_6. A prime ideal is a radical ideal. So formula_7 for any prime ideal "P". |
Minimal prime ideal | A prime ideal "P" is said to be a minimal prime ideal over an ideal "I" if it is minimal among all prime ideals containing "I". (Note: if "I" is a prime ideal, then "I" is the only minimal prime over it.) A prime ideal is said to be a minimal prime ideal if it is a minimal prime ideal over the zero ideal. |
Minimal ideal | In the branch of abstract algebra known as ring theory, a minimal right ideal of a ring "R" is a nonzero right ideal which contains no other nonzero right ideal. Likewise a minimal left ideal is a nonzero left ideal of "R" containing no other nonzero left ideals of "R", and a minimal ideal of "R" is a nonzero ideal containing no other nonzero two-sided ideal of "R". |
Radical of an ideal | If an ideal "I" coincides with its own radical, then "I" is called a "radical ideal" or "semiprime ideal". |
Monomial ideal | A toric ideal is an ideal generated by differences of monomials (provided the ideal is a prime ideal). An affine or projective algebraic variety defined by a toric ideal or a homogeneous toric ideal is an affine or projective toric variety, possibly non-normal. |
Regular ideal | In commutative algebra a regular ideal refers to an ideal containing a non-zero divisor. This article will use "regular element ideal" to help distinguish this type of ideal. |
Ideal (set theory) | In the mathematical field of set theory, an ideal is a collection of sets that are considered to be "small" or "negligible". Every subset of an element of the ideal must also be in the ideal (this codifies the idea that an ideal is a notion of smallness), and the union of any two elements of the ideal must also be in the ideal. |
Jacobian ideal | In mathematics the Jacobian ideal or gradient ideal is the ideal generated by the Jacobian of a function or function germ. |
Ideal (ring theory) | The concept of an order ideal in order theory is derived from the notion of ideal in ring theory. A fractional ideal is a generalization of an ideal, and the usual ideals are sometimes called integral ideals for clarity. |
Irrelevant ideal | In mathematics, the irrelevant ideal is the ideal of a graded ring generated by the homogeneous elements of degree greater than zero. More generally, a homogeneous ideal of a graded ring is called an irrelevant ideal if its radical contains the irrelevant ideal. |
Regular ideal | A two-sided ideal formula_1 is modular if and only if formula_8 is unital. In a unital ring, every ideal is modular since choosing "e"=1 works for any right ideal. So, the notion is more interesting for non-unital rings such as Banach algebras. From the definition it is easy to see that an ideal containing a modular ideal is itself modular. |
Ideal triangle | In hyperbolic geometry an ideal triangle is a hyperbolic triangle whose three vertices all are ideal points. Ideal triangles are also sometimes called "triply asymptotic triangles" or "trebly asymptotic triangles". The vertices are sometimes called ideal vertices. All ideal triangles are congruent. |
Ideal Film Company | The Ideal Film Company (often known as Ideal Films or simply Ideal) was a British film production and distribution company that operated between 1911 and 1934. |
Fractional ideal | the fractional ideal "J" is uniquely determined and equal to the generalized ideal quotient |
Ideal point | if all vertices of a quadrilateral are ideal points the triangle is an ideal quadrilateral. |
Ideal point | The ideal quadrilateral where the two diagonals are perpendicular to each other form an ideal square. |
Principal ideal | A ring in which every ideal is principal is called "principal", or a principal ideal ring. |
Augmentation ideal | In algebra, an augmentation ideal is an ideal that can be defined in any group ring. |
Principal ideal | A principal ideal domain (PID) is an integral domain in which every ideal is principal. |