ideal

See also: Ideal, ideał, ideál, and idéal

English

Etymology

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.

Pronunciation

• (UK) IPA^(key): /aɪˈdɪəl/
• (US) IPA^(key): /aɪˈdi(ə)l/

  • Audio (US):

    (file)

• Rhymes: -iːəl

Adjective

ideal (comparative more ideal, superlative most ideal)

1. Pertaining to ideas, or to a given idea.
2. Existing only in the mind; conceptual, imaginary.
   • 1796, Matthew Lewis, The Monk, Folio Society, published 1985, page 256:

     The idea of ghosts is ridiculous in the extreme; and if you continue to be swayed by ideal terrors —

   • 1816 June – 1817 April/May (date written), [Mary Shelley], “Chapter 4”, in Frankenstein; or, The Modern Prometheus. […], volume (please specify |volume=I to III), London: […] [Macdonald and Son] for Lackington, Hughes, Harding, Mavor, & Jones, published 1 January 1818, →OCLC:

     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 March – 1837 October, Charles Dickens, “(please specify the chapter name)”, in The Posthumous Papers of the Pickwick Club, London: Chapman and Hall, […], published 1837, →OCLC:

     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.

3. Optimal; being the best possibility.
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; […] .

5. Teaching or relating to the doctrine of idealism.

   the ideal theory or philosophy

6. (mathematics) Not actually present, but considered as present when limits at infinity are included.

   ideal point

   An ideal triangle in the hyperbolic disk is one bounded by three geodesics that meet precisely on the circle.

Synonyms

• (optimal): best, ideal, optimal, optimum
• (flawless): see also Thesaurus:flawless
• (of ideas): conceptual, notional
• (existing only in mind): conceptual, imaginary

Derived terms

• coideal
• counterideal
• hyperideal
• ideal gas
• ideal gas law
• ideal mixture
• idealness
• ideal number
• ideal point
• ideal polyhedron
• ideal-seeking behavior
• ideal solution
• ideal triangle
• ideal-typical
• idele
• nonideal
• non-ideal gas
• unideal

Related terms

• idealism
• idealistic
• ideality
• idealize
• idealless
• ideally

Translations

pertaining to ideas

• Finnish: ajatuksellinen

existing only in the mind; conceptual, imaginary

• Finnish: käsitteellinen, kuvitteellinen, ajatuksellinen

being optimal — see also optimal,‎ prime

• Afrikaans: voorbeeldig, ideaal
• Arabic: مِثَالِيّ (miṯāliyy)
• Armenian: իդեալական (hy) (idealakan)
• Asturian: ideal
• Belarusian: ідэа́льны (ideálʹny)
• Bulgarian: идеа́лен (bg) (ideálen)
• Catalan: ideal (ca)
• Chinese:

  Mandarin: 理想的 (zh) (lǐxiǎng de)

• Czech: ideální (cs)
• Dutch: ideaal (nl), optimaal (nl)
• Esperanto: ideala
• Finnish: ihanteellinen (fi), ideaalinen (fi), ideaali- (fi), optimaalinen (fi)
• French: idéal (fr)
• Galician: ideal
• German: ideal (de), bestmöglich (de), optimal (de)
• Hindi: आदर्श (hi) (ādarś), श्रेष्ठ (hi) (śreṣṭh)
• Hungarian: ideális (hu)
• Ido: ideala (io)
• Irish: idéalach
• Italian: ideale (it)
• Japanese: 理想的な (ja) (りそうてきな, risōteki na), 理想な (ja) (りそうな, risō na)
• Korean: 이상적(理想的) (ko) (isangjeok), 리상적(理想的) (risangjeok) (North Korea)
• Latvian: ideāls
• Luxembourgish: ideal
• Macedonian: идеа́лен (ideálen)
• Malayalam: ആദർശം (ml) (ādaṟśaṁ)
• Norman: idéal
• Pannonian Rusyn: идеални (idealni)
• Persian: آرمانی (fa) (ârmâni), ایده‌آل (ide-âl)
• Polish: idealny (pl) m
• Portuguese: ideal (pt)
• Russian: идеа́льный (ru) (ideálʹnyj)
• Slovak: ideálny
• Slovene: idealen
• Spanish: ideal (es), idóneo (es)
• Telugu: ఆదర్శ (te) (ādarśa)
• Ukrainian: ідеа́льний (ideálʹnyj)
• Yiddish: אידעאַל (yi) (ideal)

being perfect

• Afrikaans: ideaal
• Armenian: իդեալական (hy) (idealakan), կատարյալ (hy) (kataryal)
• Asturian: ideal
• Belarusian: ідэа́льны (ideálʹny), даскана́лы (daskanály)
• Bulgarian: съвърше́н (bg) (săvăršén), идеа́лен (bg) (ideálen)
• Catalan: ideal (ca)
• Czech: ideální (cs)
• Dutch: ideaal (nl), perfect (nl), volmaakt (nl)
• Esperanto: ideala
• Finnish: ihanteellinen (fi), ideaalinen (fi)
• French: idéal (fr), parfait (fr)
• Galician: ideal m or f
• German: ideal (de), vollendet (de), einwandfrei (de), tadellos (de), perfekt (de)
• Greek: ιδανικός (el) (idanikós)

  Ancient Greek: ἰδανικός (idanikós)

• Hindi: आदर्श (hi) (ādarś), श्रेष्ठ (hi) (śreṣṭh)
• Hungarian: tökéletes (hu), eszményi (hu)
• Ido: ideala (io)
• Irish: idéalach
• Manx: slanjeant
• Māori: takarepakore, paruhi
• Norman: idéal
• Pannonian Rusyn: идеални (idealni)
• Persian: کامل (fa) (kâmel), فربود (farbud), درست (fa) (dorost)
• Polish: idealny (pl) m
• Portuguese: ideal (pt)
• Russian: идеа́льный (ru) (ideálʹnyj), соверше́нный (ru) (soveršénnyj)
• Slovene: idealen
• Spanish: ideal (es), idóneo (es), perfecto (es)
• Telugu: ఆదర్శ (te) (ādarśa)
• Ukrainian: ідеа́льний (ideálʹnyj), доскона́лий (uk) (doskonályj)

relating to idealism

• Afrikaans: ideëel, denkbeeldig
• Armenian: երևակայական (hy) (erewakayakan), վերացական (hy) (veracʻakan)
• Asturian: ideal
• Bulgarian: въобража́ем (bg) (văobražáem), абстра́ктен (bg) (abstrákten)
• Catalan: ideal (ca)
• Dutch: ideëel (nl), conceptueel (nl)
• Esperanto: ideala
• Finnish: ideaali- (fi)
• French: idéal (fr)
• Galician: ideal
• German: ideell (de)
• Hebrew: אידיאלי (ideàli)
• Hungarian: képzelt (hu)
• Ido: ideala (io)
• Malayalam: ആദർശം (ml) (ādaṟśaṁ)
• Manx: ard-smooinagh, ard-smooinaghtagh
• Norman: idéal
• Pannonian Rusyn: идейни (idejni)
• Polish: pojęciowy (pl), konceptualny (pl)
• Portuguese: ideal (pt)
• Russian: идеа́льный (ru) (ideálʹnyj), абстра́ктный (ru) (abstráktnyj), вообража́емый (ru) (voobražájemyj)
• Slovene: idejen
• Spanish: ideal (es), conceptual (es)

math: at infinity

• Finnish: ideaalinen, ideaali-
• Persian: غایی (fa) (ġâyi)

The translations below need to be checked and inserted above into the appropriate translation tables. See instructions at Wiktionary:Entry layout § Translations.

Translations to be checked

• Esperanto: ^{(please verify)} perfekta
• Indonesian: ^{(please verify)} ideal (id)
• Interlingua: ^{(please verify)} ideal
• Italian: ^{(please verify)} ideale (it)

Noun

ideal (plural ideals)

2. A perfect standard of beauty, intellect etc., or a standard of excellence to aim at.
   • 1901 [1878], chapter 5, in Constance Garnett, transl., Anna Karenina‎^[3], translation of Анна Каренина (Anna Karenina) by Leo Tolstoy, part 6:

     Varvara Andreevna, when I was very young, I set before myself the ideal of the woman I loved and should be happy to call my wife.

   • 1945 April 16, Harry S. Truman, 9:21 from the start, in MP72-20 President Roosevelt’s Funeral and Procession; Truman – New President of U.S.‎^[4], Harry S. Truman Presidential Library and Museum, National Archives Identifier: 595162:

     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.

3. (algebra, ring theory) A two-sided ideal; a subset of a ring which is closed under both left and right multiplication by elements of the ring.

   Let $\mathbb{Z}$ be the ring of integers and let $2\mathbb{Z}$ be its ideal of even integers. Then the quotient ring $\mathbb{Z}/2\mathbb{Z}$ is a Boolean ring.

   The product of two ideals $𝔞$ and $𝔟$ is an ideal $𝔞𝔟$ which is a subset of the intersection of $𝔞$ and $𝔟$. This should help to understand why maximal ideals are prime ideals. Likewise, the union of $𝔞$ and $𝔟$ is a subset of $𝔞\mathfrak{+}𝔟$.

   • 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”, in 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.

4. (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).
   • 1992, T. S. Fofanova, “General Theory of Lattices”, in Unnamed, transl., 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.

   • 2011, George Grätzer, Lattice Theory: Foundation‎^[5], Springer (Birkhäuser), page 125:

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

   • 2015, Vijay K. Garg, Introduction to Lattice Theory with Computer Science Applications, Wiley, page 186:

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

5. (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.

   Formally, an ideal $I$ of a given set $X$ is a nonempty subset of the powerset $𝒫(X)$ such that: $(1)\mathrm{\emptyset }\in I$, $(2)A\in I\wedge B\subseteq A⟹B\in I$ and $(3)A,B\in I⟹A\cup B\in I$.

6. (algebra, Lie theory) 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.
   • 1975, Zhe-Xian Wan, translated by Che-Young Lee, Lie Algebras, Pergamon Press, page 13:

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

   • 2006, W. McGovern, “The work of Anthony Joseph in classical representation theory”, in 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:

     Next let $L$ be an arbitrary semisimple Lie algebra. Then $L$ can be written uniquely as a direct sum $L_1\oplus \cdots \oplus L_t$ of simple ideals (Theorem 5.2).

7. (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.

   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.

Synonyms

• (order theory): order ideal
• (type of Lie subalgebra): Lie ideal

Antonyms

• (antonym(s) of “order theory”): filter

Hyponyms

• (mathematics): maximal ideal, principal ideal

Derived terms

• different ideal
• factor ideal
• fractional ideal
• Frink ideal
• ideal lattice
• lattice ideal
• left ideal
• minimal ideal
• Platonic ideal
• primary ideal
• prime ideal
• principal ideal
• principal ideal domain
• principal ideal ring
• pseudoideal
• radical ideal
• right ideal
• subideal
• two-sided ideal
• vanishing ideal
• zero ideal

Translations

perfect standard of beauty, intellect etc.

• Afrikaans: ideaal
• Asturian: ideal m
• Belarusian: ідэа́л m (ideál)
• Bulgarian: идеа́л (bg) m (ideál)
• Catalan: ideal (ca) m
• Chinese:

  Mandarin: 典范 (zh) (diǎnfàn), 理想 (zh) (lǐxiǎng)

• Czech: ideál m
• Dutch: ideaal (nl) n, perfectie (nl) f, streefdoel (nl) n
• Esperanto: idealo (eo), perfekta
• Finnish: ihanne (fi), ideaali (fi)
• French: idéal (fr) m
• Galician: ideal m
• German: Ideal (de) n, Idealbild (de) n
• Greek: ιδεώδες (el) n (ideódes)
• Hebrew: אידיאל \ אִידֵאָל (he) (ide'ál)
• Hindi: आदर्श (hi) m (ādarś), श्रेष्ठ (hi) m (śreṣṭh)
• Hungarian: eszmény (hu), ideál (hu), mintakép (hu)
• Ido: idealo (io)
• Indonesian: ideal (id)
• Interlingua: ideal
• Irish: idéal m
• Italian: ideale (it) m
• Japanese: 理想 (ja) (りそう, risō)
• Kazakh: мұрат (kk) (murat)
• Korean: 이상(理想) (ko) (isang), 리상(理想) (ko) (risang) (North Korea)
• Persian: آرمان (fa) (ârmân), ایدئال (ide'âl)
• Polish: ideał (pl) m
• Portuguese: ideal (pt) m
• Punjabi: ਆਦਰਸ਼ (pa) m (ādarś)
• Russian: идеа́л (ru) m (ideál)
• Slovak: ideál m
• Slovene: ideal m
• Spanish: ideal (es) m, canon (es) m
• Swedish: ideal (sv) n
• Telugu: ఆదర్శం (te) (ādarśaṁ)
• Turkish: ideal (tr), mefkûre (tr), ülkü (tr)
• Ukrainian: ідеа́л m (ideál)
• Vietnamese: lý tưởng (vi)
• Welsh: delfryd (cy) m or f
• Yiddish: אידעאַל (yi) (ideal)

subring closed under multiplication by containing ring

• Chinese:

  Mandarin: 理想 (zh) (lǐxiǎng)

• Dutch: ideaal (nl) n
• Finnish: ideaali (fi)
• French: idéal (fr) m
• German: Ideal (de) n
• Japanese: イデアル (ja) (idearu)
• Kazakh: идеал (ıydeal)
• Polish: ideał (pl) m
• Romanian: ideal (ro) n
• Russian: идеа́л (ru) m (ideál)
• Swedish: ideal (sv) n

lower set closed under joins

• Chinese:

  Mandarin: 理想 (zh) (lǐxiǎng)

• Irish: idéal m
• Russian: идеа́л (ru) m (ideál)

unattainable state

• German: Idealzustand (de) m
• Polish: ideał (pl) m
• Russian: идеа́л (ru) m (ideál)

Further reading

• Ideal (ring theory) on Wikipedia.Wikipedia
• Ideal (order theory) on Wikipedia.Wikipedia
• Ideal (set theory) on Wikipedia.Wikipedia
• Ideal point on Wikipedia.Wikipedia
• Ideal triangle on Wikipedia.Wikipedia
• Lie algebra on Wikipedia.Wikipedia

Anagrams

• Delia, Elida, ailed, ladie

Asturian

Etymology

From Latin ideālis.

Pronunciation

• IPA^(key): /ideˈal/ [i.ð̞eˈal]
• Rhymes: -al
• Syllabification: i‧de‧al

Adjective

ideal (epicene, plural ideales)

1. ideal

Noun

ideal m (plural ideales)

1. ideal

Further reading

• “ideal (noun)”, in Diccionariu de la llingua asturiana [Dictionary of the Asturian Language] (in Asturian), 1st edition, Academy of the Asturian Language [Asturian: Academia de la Llingua Asturiana], 2000, →ISBN
• “ideal (adjective)”, in Diccionariu de la llingua asturiana [Dictionary of the Asturian Language] (in Asturian), 1st edition, Academy of the Asturian Language [Asturian: Academia de la Llingua Asturiana], 2000, →ISBN

Catalan

Etymology

Learned borrowing from Latin ideālis.

Pronunciation

• IPA^(key): (Northern) [i.ðe̞ˈal]
• IPA^(key): (Balearic, Central, Valencia, Northwestern) [i.ðeˈal]

• Audio (Barcelona):

  (file)

Adjective

ideal m or f (masculine and feminine plural ideals)

1. ideal

Derived terms

• idealisme
• idealista
• idealitat
• idealitzar
• idealment

Noun

ideal m (plural ideals)

1. ideal

Chavacano

Etymology

Inherited from Spanish ideal (“ideal”).

Pronunciation

• Hyphenation: i‧de‧al

Adjective

ideal

1. ideal

Related terms

• idea

Danish

Etymology 1

From Late Latin ideālis, from Latin idea.

Adjective

ideal (neuter idealt, plural and definite singular attributive ideale)

1. ideal

   Synonyms: perfekt, fuldkommen

   Coordinate term: ideel

Inflection

Inflection of ideal

	positive	comparative	superlative
indefinite common singular	ideal	mere ideal	mest ideal2
indefinite neuter singular	idealt	mere ideal	mest ideal2
plural	ideale	mere ideal	mest ideal2
definite attributive1	ideale	mere ideal	mest ideale

¹ When an adjective is applied predicatively to something definite,
the corresponding "indefinite" form is used.
² The "indefinite" superlatives may not be used attributively.

Derived terms

• idealisere
• idealisme
• idealist

Etymology 2

A nominalization of the adjective above.

Noun

ideal n (singular definite idealet, plural indefinite idealer)

1. ideal (quality)
2. role model, exemplar (person or thing)

   Synonym: forbillede

Declension

Declension of ideal

neuter gender	singular		plural
	indefinite	definite	indefinite	definite
nominative	ideal	idealet	idealer	idealerne
genitive	ideals	idealets	idealers	idealernes

Derived terms

• skønhedsideal
• frihedsideal
• kvindeideal

Further reading

• “ideal” in Den Danske Ordbog

Galician

Etymology

Etymology tree

Proto-Indo-European *weyd-der.

Ancient Greek ῐ̓δεῖν (ĭdeîn)

Ancient Greek ἰδέα (idéa)der.

Latin idea

Proto-Indo-European *h₂el-

Proto-Indo-European *-is

Proto-Indo-European *h₂élisder.?

Proto-Italic *-ālis

Latin -ālis

Latin ideālisder.

Galician ideal

Derived from Latin ideālis.

Pronunciation

• IPA^(key): /idɛˈal/ [i.ð̞ɛˈɑɫ]
• Rhymes: -al
• Hyphenation: i‧de‧al

Adjective

ideal m or f (plural ideais)

1. ideal

Derived terms

• idealmente

Noun

ideal m (plural ideais)

1. ideal

Further reading

• “ideal”, in Dicionario da Real Academia Galega (in Galician), A Coruña: Royal Galician Academy, 2012–2026
• “ideal”, in Dicionário Estraviz de galego (in Galician), 2014–2026

German

Etymology

Borrowed from Late Latin ideālis (“existing in idea”), from Latin idea (“idea”). Doublet of ideell.

Pronunciation

• IPA^(key): /ideˈaːl/
• Rhymes: -aːl

• Audio (Germany (Berlin)):

  (file)

Adjective

ideal (strong nominative masculine singular idealer, comparative (colloquial) idealer, superlative (colloquial) am idealsten)

1. ideal (optimal, perfect)

Declension

Positive forms of ideal number & gender singular plural masculine feminine neuter predicative er ist ideal sie ist ideal es ist ideal sie sind ideal strong declension (without article) nominative idealer ideale ideales ideale genitive idealen idealer idealen idealer dative idealem idealer idealem idealen accusative idealen ideale ideales ideale weak declension (with definite article) nominative der ideale die ideale das ideale die idealen genitive des idealen der idealen des idealen der idealen dative dem idealen der idealen dem idealen den idealen accusative den idealen die ideale das ideale die idealen mixed declension (with indefinite article) nominative ein idealer eine ideale ein ideales (keine) idealen genitive eines idealen einer idealen eines idealen (keiner) idealen dative einem idealen einer idealen einem idealen (keinen) idealen accusative einen idealen eine ideale ein ideales (keine) idealen Comparative forms of ideal number & gender singular plural masculine feminine neuter predicative er ist idealer sie ist idealer es ist idealer sie sind idealer strong declension (without article) nominative idealerer idealere idealeres idealere genitive idealeren idealerer idealeren idealerer dative idealerem idealerer idealerem idealeren accusative idealeren idealere idealeres idealere weak declension (with definite article) nominative der idealere die idealere das idealere die idealeren genitive des idealeren der idealeren des idealeren der idealeren dative dem idealeren der idealeren dem idealeren den idealeren accusative den idealeren die idealere das idealere die idealeren mixed declension (with indefinite article) nominative ein idealerer eine idealere ein idealeres (keine) idealeren genitive eines idealeren einer idealeren eines idealeren (keiner) idealeren dative einem idealeren einer idealeren einem idealeren (keinen) idealeren accusative einen idealeren eine idealere ein idealeres (keine) idealeren Superlative forms of ideal number & gender singular plural masculine feminine neuter predicative er ist am idealsten sie ist am idealsten es ist am idealsten sie sind am idealsten strong declension (without article) nominative idealster idealste idealstes idealste genitive idealsten idealster idealsten idealster dative idealstem idealster idealstem idealsten accusative idealsten idealste idealstes idealste weak declension (with definite article) nominative der idealste die idealste das idealste die idealsten genitive des idealsten der idealsten des idealsten der idealsten dative dem idealsten der idealsten dem idealsten den idealsten accusative den idealsten die idealste das idealste die idealsten mixed declension (with indefinite article) nominative ein idealster eine idealste ein idealstes (keine) idealsten genitive eines idealsten einer idealsten eines idealsten (keiner) idealsten dative einem idealsten einer idealsten einem idealsten (keinen) idealsten accusative einen idealsten eine idealste ein idealstes (keine) idealsten

Derived terms

• idealerweise

Further reading

• “ideal” in Duden online
• “ideal”, in Digitales Wörterbuch der deutschen Sprache‎^[6] (in German)

Indonesian

Etymology

From Dutch ideaal, from French idéal, from Medieval Latin ideālis.

Pronunciation

• (Standard Indonesian) IPA^(key): /iˈdeal/ [iˈde.al]
• Rhymes: -eal
• Syllabification: i‧de‧al

Adjective

idéal (comparative lebih ideal, superlative paling ideal)

1. ideal; optimal, being the best possibility
2. ideal; pertaining to ideas, or to a given idea

Noun

idéal (plural ideal-ideal)

1. (mathematics) ideal; a subring closed under multiplication by its containing ring

Alternative forms

• idiil (noun)

Derived terms

• mengidealkan

Related terms

• ide

Further reading

• “ideal”, in Kamus Besar Bahasa Indonesia [Great Dictionary of the Indonesian Language] (in Indonesian), Jakarta: Agency for Language Development and Cultivation – Ministry of Education, Culture, Research, and Technology of the Republic of Indonesia, 2016

Luxembourgish

Pronunciation

• IPA^(key): /ideˈaːl/, [idəˈaːl], /idiˈaːl/

Adjective

ideal (masculine idealen, neuter ideaalt, comparative méi ideal, superlative am ideaalsten)

1. ideal

Declension

Declension of ideal

		singular			plural
		masculine	feminine	neuter
predicative		hien ass ideal	si ass ideal	et ass ideal	si si(nn) ideal
nominative / accusative	attributive and/or after determiner	idealen	ideal	ideaalt	ideal
	independent without determiner			ideales	idealer
dative	after any declined word	idealen	idealer	idealen	idealen
	as first declined word	idealem		idealem

Norwegian Bokmål

Etymology

From French idéal, from Late Latin ideālis (“existing in idea”), from Latin idea (“idea”).

Noun

ideal n (definite singular idealet, indefinite plural ideal or idealer, definite plural ideala or idealene)

1. ideal
   • 1886, Henrik Ibsen, Vildanden:

     Brug ikke det udenlandske ord: idealer. Vi har jo det gode norske ord: løgne.

     Do not use the foreign word: ideals. We have, as you may know, the good Norwegian word: lies.

References

• “ideal” in The Bokmål Dictionary.

Norwegian Nynorsk

Etymology

From French idéal, from Late Latin ideālis (“existing in idea”), from Latin idea (“idea”).

Noun

ideal n (definite singular idealet, indefinite plural ideal, definite plural ideala)

1. ideal

References

• “ideal” in The Nynorsk Dictionary.

Piedmontese

Pronunciation

• IPA^(key): /ideˈal/

Adjective

ideal

1. ideal

Noun

ideal m

1. ideal

Portuguese

Etymology

Etymology tree

Proto-Indo-European *weyd-der.

Ancient Greek ῐ̓δεῖν (ĭdeîn)

Ancient Greek ἰδέα (idéa)der.

Latin idea

Proto-Indo-European *h₂el-

Proto-Indo-European *-is

Proto-Indo-European *h₂élisder.?

Proto-Italic *-ālis

Latin -ālis

Latin ideālislbor.

Portuguese ideal

Learned borrowing from Latin ideālis. By surface analysis, ideia + -al.

Pronunciation

• (Brazil) IPA^(key): /i.deˈaw/ [i.deˈaʊ̯]

 

• (Portugal) IPA^(key): /iˈdjal/ [iˈðjaɫ]

• (Portugal) IPA^(key): /iˈdjal/ [iˈðjaɫ]
  • (Southern Portugal) IPA^(key): /iˈdja.li/

• Rhymes: -al, -aw
• Hyphenation: i‧de‧al

Adjective

ideal m or f (plural ideais)

1. ideal
2. notional

Derived terms

• idealmente

Noun

ideal m (plural ideais)

1. ideal
2. fantasy

Further reading

• “ideal”, in Dicionário Priberam da Língua Portuguesa (in Portuguese), Lisbon: Priberam, 2008–2026

Romanian

Etymology

Etymology tree

Proto-Indo-European *weyd-der.

Ancient Greek ῐ̓δεῖν (ĭdeîn)

Ancient Greek ἰδέα (idéa)der.

Latin idea

Proto-Indo-European *h₂el-

Proto-Indo-European *-is

Proto-Indo-European *h₂élisder.?

Proto-Italic *-ālis

Latin -ālis

Latin idealis

French idéalbor.

Romanian ideal

Borrowed from French idéal, from Latin idealis.

Pronunciation

• Audio:

  (file)

Adjective

ideal m or n (feminine singular ideală, masculine plural ideali, feminine/neuter plural ideale)

1. ideal

Declension

Declension of ideal

		singular			plural
		masculine	neuter	feminine	masculine	neuter	feminine
nominative- accusative	indefinite	ideal		ideală	ideali	ideale
	definite	idealul		ideala	idealii	idealele
genitive- dative	indefinite	ideal		ideale	ideali	ideale
	definite	idealului		idealei	idealilor	idealelor

Related terms

• idealism
• idealist
• idealiza

Serbo-Croatian

Pronunciation

• IPA^(key): /iděaːl/
• Hyphenation: i‧de‧al

Noun

idèāl m inan (Cyrillic spelling идѐа̄л)

1. ideal

Declension

Declension of ideal

	singular	plural
nominative	idèāl	ideali
genitive	ideála	ideala
dative	idealu	idealima
accusative	ideal	ideale
vocative	ideale	ideali
locative	idealu	idealima
instrumental	idealom	idealima

Spanish

Etymology

Etymology tree

Proto-Indo-European *weyd-der.

Ancient Greek ῐ̓δεῖν (ĭdeîn)

Ancient Greek ἰδέα (idéa)der.

Latin idea

Proto-Indo-European *h₂el-

Proto-Indo-European *-is

Proto-Indo-European *h₂élisder.?

Proto-Italic *-ālis

Latin -ālis

Latin ideālisder.

Spanish ideal

Derived from Latin ideālis.

Pronunciation

• IPA^(key): /ideˈal/ [i.ð̞eˈal]
• Rhymes: -al
• Syllabification: i‧de‧al

Adjective

ideal m or f (masculine and feminine plural ideales)

1. ideal

Derived terms

• idealidad
• idealizar
• idealmente

Noun

ideal m (plural ideales)

1. ideal

Further reading

• “ideal”, in Diccionario de la lengua española [Dictionary of the Spanish Language] (in Spanish), online version 23.8.1, Royal Spanish Academy [Spanish: Real Academia Española], 15 December 2025

Swedish

Pronunciation

• Audio:

  (file)

Adjective

ideal (not comparable)

1. ideal (perfect)

   Synonym: idealisk

   under ideala förhållanden

   under ideal conditions

Declension

Inflection of ideal

Indefinite	positive	comparative	superlative1
common singular	ideal	—	—
neuter singular	idealt	—	—
plural	ideala	—	—
masculine plural2	ideale	—	—
Definite	positive	comparative	superlative
masculine singular3	ideale	—	—
all	ideala	—	—

¹ The indefinite superlative forms are only used in the predicative.
² Dated or archaic.
³ Only used, optionally, to refer to things whose natural gender is masculine.

Noun

ideal n

1. ideal; perfect standard
2. (mathematics) ideal; special subsets of a ring

Declension

Declension of ideal

		nominative	genitive
singular	indefinite	ideal	ideals
	definite	idealet	idealets
plural	indefinite	ideal	ideals
	definite	idealen	idealens

Related terms

• idé
• idealisera
• idealisk
• idealism
• idealist
• idealistisk

References

• “ideal”, in Svensk ordbok [Dictionary of Swedish] (in Swedish)
• “ideal”, in Svenska Akademiens ordlista [Wordlist of the Swedish Academy] (in Swedish)
• “ideal”, in Svenska Akademiens ordbok [Dictionary of the Swedish Academy] (in Swedish)

Anagrams

• ilade

Tagalog

Alternative forms

• ideyal

Etymology

Etymology tree

Proto-Indo-European *weyd-der.

Ancient Greek ῐ̓δεῖν (ĭdeîn)

Ancient Greek ἰδέα (idéa)der.

Latin idea

Proto-Indo-European *h₂el-

Proto-Indo-European *-is

Proto-Indo-European *h₂élisder.?

Proto-Italic *-ālis

Latin -ālis

Latin ideālisder.

Spanish idealbor.

Tagalog ideal

Borrowed from Spanish ideal.

Pronunciation

• (Standard Tagalog) IPA^(key): /ʔideˈal/ [ʔɪ.d̪ɛˈjal]
• Rhymes: -al
• Syllabification: i‧de‧al

Noun

ideál (Baybayin spelling ᜁᜇᜒᜌᜎ᜔)

1. ideal (model to be imitated)

   Synonyms: huwaran, uliran

2. ambition

   Synonyms: mithi, mithiin, pangarap, ambisyon

Related terms

• idea
• idealismo
• idealista

Adjective

ideál (Baybayin spelling ᜁᜇᜒᜌᜎ᜔)

1. ideal (just as what one wants)
2. worthy of imitation

   Synonym: uliran

Turkish

Etymology

Borrowed from French idéal.

Pronunciation

• IPA^(key): /ideˈɑl/
• Hyphenation: i‧de‧al

Adjective

ideal

1. ideal

Noun

ideal (definite accusative ideali, plural idealler)

1. ideal

Declension

Declension of ideal

singular plural nominative ideal idealler definite accusative ideali idealleri dative ideale ideallere locative idealde ideallerde ablative idealden ideallerden genitive idealin ideallerin Possessive forms nominative singular plural 1st singular idealim ideallerim 2nd singular idealin ideallerin 3rd singular ideali idealleri 1st plural idealimiz ideallerimiz 2nd plural idealiniz idealleriniz 3rd plural idealleri idealleri definite accusative singular plural 1st singular idealimi ideallerimi 2nd singular idealini ideallerini 3rd singular idealini ideallerini 1st plural idealimizi ideallerimizi 2nd plural idealinizi ideallerinizi 3rd plural ideallerini ideallerini dative singular plural 1st singular idealime ideallerime 2nd singular idealine ideallerine 3rd singular idealine ideallerine 1st plural idealimize ideallerimize 2nd plural idealinize ideallerinize 3rd plural ideallerine ideallerine locative singular plural 1st singular idealimde ideallerimde 2nd singular idealinde ideallerinde 3rd singular idealinde ideallerinde 1st plural idealimizde ideallerimizde 2nd plural idealinizde ideallerinizde 3rd plural ideallerinde ideallerinde ablative singular plural 1st singular idealimden ideallerimden 2nd singular idealinden ideallerinden 3rd singular idealinden ideallerinden 1st plural idealimizden ideallerimizden 2nd plural idealinizden ideallerinizden 3rd plural ideallerinden ideallerinden genitive singular plural 1st singular idealimin ideallerimin 2nd singular idealinin ideallerinin 3rd singular idealinin ideallerinin 1st plural idealimizin ideallerimizin 2nd plural idealinizin ideallerinizin 3rd plural ideallerinin ideallerinin Predicative forms singular plural 1st singular idealim ideallerim 2nd singular idealsin ideallersin 3rd singular ideal idealdir idealler ideallerdir 1st plural idealiz idealleriz 2nd plural idealsiniz ideallersiniz 3rd plural idealler ideallerdir

Synonyms

• ülkü

Welsh

Alternative forms

• ideol

Etymology

Borrowed from English ideal.

Pronunciation

• IPA^(key): /ɪˈdɛal/

Adjective

ideal (feminine singular ideal, plural ideal, not comparable)

1. ideal

   Synonym: delfrydol

Noun

ideal m (plural idealau)

1. ideal

   Synonym: delfryd

Mutation

Mutated forms of ideal

radical	soft	nasal	h-prothesis
ideal	unchanged	unchanged	hideal

Note: Certain mutated forms of some words can never occur in standard Welsh.
All possible mutated forms are displayed for convenience.