Meaning of ideal | Babel Free

Definitions

1. A perfect standard of beauty, intellect etc., or a standard of excellence to aim at.
2. A city in Georgia, United States.
3. A two-sided ideal; a subset of a ring which is closed under both left and right multiplication by elements of the ring.
4. An unincorporated community in Illinois.
5. perfect. This tool is ideal for the job I have in mind. ideaal مِثالي идеален ideal ideální ideal ideel ιδεώδης, ιδανικόςideal täiuslik ایده آل ideaali idéalמושלם पूर्ण, आदर्श idealan eszményi, ideális sempurna fullkominn ideale 理想的な 완벽한 idealus ideāls; pilnīgs sempurna ideaalideell, perfekt, mønstergyldigidealny ايډيالى، خيالى، تصورى، عقلى: دژوند هدف، نصب العين، وروستۍ هيله، ارمان ideal ideal идеальный ideálny idealen idealan idealisk ดีเลิศ ideal, mükemmel 理想的 ідеальний, досконалий معیاری l...
6. A non-empty lower set (of a partially ordered set) which is closed under binary suprema (a.k.a. joins).
7. An unincorporated community in South Dakota.
8. a person having (too) high ideals of behaviour etc. idealis مِثالي идеалист idealista idealista der/die Idealist(in) idealist ιδεαλιστήςidealista idealist آدم آرمان گرا idealisti idéalisteאידיאליסט आदर्शवादी idealist idealista idealis hugsjónamaður idealista 理想主義者 이상주의자 idealistas ideālists idealis idealistidealistidealista دايډيا ليزم دفلسفى پر خوا idealista idealist идеалист idealista idealist idealista idealist ผู้ยึดมั่นอุดมการณ์ ülkücü, idealist 理想主義者 ідеаліст عینیت پسند người hay lý tưở...
   etc
9. 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.
10. idealisme مِثالِيَّه идеализъм idealismo idealismus der Idealismus idealisme ιδεαλισμόςidealismo idealism آرمان گرایی idealismi idéalismeאידיאליסט आदर्शवाद idealizam idealizmus idealisme hugsjónastefna; hughyggja idealismo 理想主義 이상주의 idealizmas ideālisms idealisme idealismeidealisme idealizm ايډياليزم، دتصور داصالت فلسفه (هغه فلسفى متكب چې فكر تر مادى مقدم بولى idealismo idealism идеализм idealizmus idealizem idealizam idealism อุดมคตินิยม ülkücülük, idealizm 理想主義 ідеалізм مثالیت chủ nghĩa duy...
11. 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.
12. idealisties مِثالي идеалистичен idealista idealistický idealistisch idealistisk ιδεαλιστικόςidealista idealistlik آرمان گرایانه idealistinen idéaliste אִיֵדיאָלִיסטִי आदर्शवादी idealistički idealista, idealisztikus idealistis hugsjóna- idealistico 理想主義の 이상주의의 idealistinis ideālistisks idealistik idealistischidealistiskidealistyczny فكرى، معنوى، تصورى idealista idealist идеалистический idealistický idealističen idealističan idealistisk ซึ่งยึดมั่นอุดมการณ์ ülkücü, idealist 理想主義的 ідеалістичний ...
13. 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.
14. to regard as perfect. Children tend to idealize their parents. idealiseer يَجْعَلُ مِثالِيّا идеализирам idealizar idealizovat (si) idealisieren idealisere εξιδανικεύωidealizar idealiseerima بی کاستی پنداشتن ihannoida idéaliser לַעֲשוֹת אִידֵיאָלִיזַציה שֶל आदर्शीकरण करना, आदर्श के रूप में प्रस्तुत करना idealizirati eszményít, idealizál menganggap sempurna líta á sem fullkominn; fegra idealizzare 理想化する 이상적인 것으로서 여기다 idealizuoti idealizēt menganggap sempurna idealiserenidealisere, forgude idea...
15. idealisering جَعْل الشَّخص أو الشَّيء مِثالِيّا идеализация idealização idealizace die Idealisierung idealisering εξιδανίκευσηidealización idealiseerimine آرمان گرایی ihannointi idéalisation אִידֵיאָלִיזַציה आदर्शीकरण idealizacija eszményítés, idealizálás menganggap sempurna fegrun, gylling idealizzazione 理想化 이상화 idealizavimas idealizēšana; idealizācija kesempurnaan idealiseringidealisering, forguding idealizacja ايډياليزم، دتصور داصالت فلسفه (هغه فلسفى متكب چې فكر تر مادى مقدم بولى idealizaç...
16. , a. ideal; perfecto-a.
17. A conception of something in its absolute perfection: the ideal of national unity.
18. One that is regarded as a standard or model of perfection or excellence: The restaurant is considered the ideal in fine dining.
19. An ultimate or worthy object of endeavor; a goal: "those who regarded even a rhetorical commitment to the ideal of disarmament as irresponsibly utopian" (James Carroll).

Equivalents

Examples

“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”

“With great humility, I call upon all Americans to help me keep our nation united in defense of those ideals which have been so eloquently proclaimed by Franklin Roosevelt. I want in turn to assure my fellow Americans and all of those who love peace and liberty throughout the world that I will support and defend those ideals with all my strength and all my heart.”

“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;.”

“In trying to understand the ideal theory of a commutative ring, one quickly sees that it is important to first understand the prime ideals.”

“If an ideal I of a ring contains the multiplicative identity 1, then we have seen that I must be the entire ring.”

“However, every R has a minimal prime ideal consisting of left zero-divisors and one of right zero-divisors.”

“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.”

“1.35 Find a distributive lattice L with no minimal and no maximal prime ideals.”

“Definition 15.11 (Width Ideal) An ideal Q of a poset P = (X,≤) is a width ideal if maximal(Q) is a width antichain.”

“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.”

“If 𝖌 is a Lie algebra, 𝖍 is an ideal and the Lie algebras 𝖍 and 𝖌/𝖍 are solvable, then 𝖌 is solvable.”

“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.”

“Next let L be an arbitrary semisimple Lie algebra. Then L can be written uniquely as a direct sum L#95;1#92;oplus#92;dots#92;oplusL#95;t of simple ideals (Theorem 5.2).”

“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.”

CEFR level