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意味・対訳 理想、極致、理想的なもの、典型、崇高な目標
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ideal
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He's the ideal of the aggressive salesman. 彼は積極的なセールスマンの典型だ. |
宗教・哲学のほかの用語一覧
「ideal」を含む例文一覧
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The ideal environment例文帳に追加
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ハイパー英語辞書での「ideal」の意味 |
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Wiktionary英語版での「ideal」の意味 |
ideal
語源
From French idéal, from Late Latin ideālis (“existing in idea”), from Latin idea (“idea”); see idea.
In mathematics, the noun ring theory sense was first introduced by German mathematician Richard Dedekind in his 1871 edition of a text on number theory. The concept was quickly expanded to ring theory and later generalised to order theory. The set theory and Lie theory senses can be regarded as applications of the order theory sense.
形容詞
ideal (comparative more ideal, superlative most ideal)
- Optimal; being the best possibility.
- Perfect, flawless, having no defects.
- 1751 April 13, Samuel Johnson, The Rambler, Number 112, reprinted in 1825, The Works of Samuel Johnson, LL. D., Volume 1, Jones & Company, page 194,
- There will always be a wide interval between practical and ideal excellence; […] .
- 1751 April 13, Samuel Johnson, The Rambler, Number 112, reprinted in 1825, The Works of Samuel Johnson, LL. D., Volume 1, Jones & Company, page 194,
- Pertaining to ideas, or to a given idea.
- Existing only in the mind; conceptual, imaginary.
- 1796, Matthew Lewis, The Monk, Folio Society 1985, p. 256:
- The idea of ghosts is ridiculous in the extreme; and if you continue to be swayed by ideal terrors —
- 1818, Mary Shelley, Frankenstein, or the Modern Prometheus,[2] Chapter 4,
- Life and death appeared to me ideal bounds, which I should first break through, and pour a torrent of light into our dark world.
- 1836-37, Charles Dickens, The Pickwick Papers
- At first, he began to doubt the reality of his adventures, but the acute pain in his shoulders when he attempted to rise, assured him that the kicking of the goblins was certainly not ideal.
- 1796, Matthew Lewis, The Monk, Folio Society 1985, p. 256:
- Teaching or relating to the doctrine of idealism.
- (mathematics) Not actually present, but considered as present when limits at infinity are included.
- ideal point
同意語
名詞
- 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.
- Let be the ring of integers and let be its ideal of even integers. Then the quotient ring is a Boolean ring.
- The product of two ideals and is an ideal which is a subset of the intersection of and . This should help to understand why maximal ideals are prime ideals. Likewise, the union of and is a subset of .
- 2004, K. R. Goodearl, R. B. Warfield, Jr., An Introduction to Noncommutative Noetherian Rings, 2nd Edition, Cambridge University Press, page 47,
- In trying to understand the ideal theory of a commutative ring, one quickly sees that it is important to first understand the prime ideals.
- 2009, John J. Watkins, Topics in Commutative Ring Theory, Princeton University Press, page 45,
- If an ideal I of a ring contains the multiplicative identity 1, then we have seen that I must be the entire ring.
- 2010, W. D. Burgess, A. Lashgari, A. Mojiri, Elements of Minimal Prime Ideals in General Rings, Sergio R. López-Permouth, Dinh Van Huynh (editors), Advances in Ring Theory, Springer (Birkhäuser), page 69,
- However, every R has a minimal prime ideal consisting of left zero-divisors and one of right zero-divisors.
- (algebra, order theory, lattice theory) A non-empty lower set (of a partially ordered set) which is closed under binary suprema (a.k.a. joins).[1]
- 1992, Unnamed translator, T. S. Fofanova, General Theory of Lattices, in Ordered Sets and Lattices II, American Mathematical Society, page 119,
- 2011, George Grätzer, Lattice Theory: Foundation, Springer (Birkhäuser), page 125,
- 2015, Vijay K. Garg, Introduction to Lattice Theory with Computer Science Applications, Wiley, page 186,
- (set theory) 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.
- (algebra, Lie theory) A Lie subalgebra (subspace that is closed under the Lie bracket) of a given Lie algebra such that the Lie bracket [,] is a subset of .
- 1975, Che-Young Lee (translator), Zhe-Xian Wan, Lie Algebras, Pergamon Press, page 13,
- If is a Lie algebra, is an ideal and the Lie algebras and / are solvable, then is solvable.
- 2006, W. McGovern, The work of Anthony Joseph in classical representation theory, Anthony Joseph, Joseph Bernstein, Vladimir Hinich, Anna Melnikov (editors), Studies in Lie Theory: Dedicated to A. Joseph on His Sixtieth Birthday, Springer (Birkhäuser), page 3,
- What really put primitive ideals in enveloping algebras of semisimple Lie algebras on the map was Duflo's fundamental theorem that any such ideal is the annihilator of a very special kind of simple module, namely a highest weight module.
- 2013, J.E. Humphreys, Introduction to Lie Algebras and Representation Theory, Springer, page 73,
- 1975, Che-Young Lee (translator), Zhe-Xian Wan, Lie Algebras, Pergamon Press, page 13,
- (algebra) 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.[2]
- The set of natural numbers with multiplication as the monoid operation (instead of addition) has multiplicative ideals, such as, for example, the set {1, 3, 9, 27, 81, ...}. If any member of it is multiplied by a number which is not a power of 3 then the result will not be a power of three.
下位語
派生語
- ideal lattice
- lattice ideal
- left ideal
- Platonic ideal
- prime ideal
- principal ideal
- pseudoideal
- right ideal
- subideal
- two-sided ideal
参照
- ^ Boolean prime ideal theorem#Prime ideal theorems on Wikipedia.
- ^ Vaughan Pratt (2004) Chapter 1 : Lattice Theory[1], boole.stanford.edu, §1.3.5
Further reading
- Ideal (ring theory) on Wikipedia.
- Ideal (order theory) on Wikipedia.
- Ideal (set theory) on Wikipedia.
- Ideal point on Wikipedia.
- Ideal triangle on Wikipedia.
- Lie algebra#Subalgebras, ideals and homomorphisms on Wikipedia.
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