ideal
n. 理想, 典范, 观念, 思想, 最后目标 a. 理想的, 完美的, 空想的, 观念的, 唯心论的
发音
词形变化
教材释义与例句
理想；典范
理想的；完美的；想象的；不切实际的
释义与例句
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1.
A perfect standard of beauty, intellect etc., or a standard of excellence to aim at.
典范
理想
Ideals are like stars; you will not succeed in touching them with your hands. But like the seafaring man on the desert of waters, you choose them as your guides, and following them you will reach your destiny - Carl Schurz
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2.
A two-sided ideal; a subset of a ring which is closed under both left and right multiplication by elements of the ring.
理想
数学Let #92;mathbb#123;Z#125; be the ring of integers and let 2#92;mathbb#123;Z#125; be its ideal of even integers. Then the quotient ring #92;mathbb#123;Z#125;#47;2#92;mathbb#123;Z#125; is a Boolean ring.
The product of two ideals #92;mathfrak#123;a#125; and #92;mathfrak#123;b#125; is an ideal #92;mathfrak#123;ab#125; which is a subset of the intersection of #92;mathfrak#123;a#125; and #92;mathfrak#123;b#125;. This should help to understand why maximal ideals are prime ideals. Likewise, the union of #92;mathfrak#123;a#125; and #92;mathfrak#123;b#125; is a subset of #92;mathfrak#123;a#43;b#125;.
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3.
A non-empty lower set (of a partially ordered set) which is closed under binary suprema (a.k.a. joins).
理想
数学1992, Unnamed translator, T. S. Fofanova, General Theory of Lattices, in Ordered Sets and Lattices II, American Mathematical Society, page 119, An ideal A of L is called complete if it contains all least upper bounds of its subsets that exist in L. Bishop and Schreiner [80] studied conditions under which joins of ideals in the lattices of all ideals and of all complete ideals coincide.
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4.
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.
数学Formally, an ideal I of a given set X is a nonempty subset of the powerset #92;mathcal#123;P#125;(X) such that: (1)#92;#92;emptyset#92;inI, (2)#92;A#92;inI#92;andB#92;subseteqA#92;impliesB#92;inI and (3)#92;A,B#92;inI#92;impliesA#92;cupB#92;inI.
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5.
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.
数学 -
6.
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.
数学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.
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1.
Pertaining to ideas, or to a given idea.
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2.
Existing only in the mind; conceptual, imaginary.
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3.
Optimal; being the best possibility.
理想的
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4.
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; […] .
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5.
Teaching or relating to the doctrine of idealism.
the ideal theory or philosophy
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6.
Not actually present, but considered as present when limits at infinity are included.
数学ideal point
An ideal triangle in the hyperbolic disk is one bounded by three geodesics that meet precisely on the circle.
词汇关系
同义词 6
上位词 4
下位词 10
同义词 1
近义相关 2
相关短语
词源
From French idéal, from Late Latin ideālis (“existing in idea”), by surface analysis, idea + -al, 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.
来源：wiktionary