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Words, grammatical forms and meanings linked to the ontology.

algebra en · NOUN

Pronunciation

  • /ˈæl.d͡ʒə.bɹə/ (US)
  • (US) audio
  • /ˈæl.dʒɪ.bɹə/ (UK)
  • /ˈæl.d͡ʒɪ.bɹə/ (US)

Etymology

Etymology tree Arabic جَبَرَ (jabara) Arabic الْجَبْر (al-jabr)bor. Medieval Latin algebrabor. English algebra Borrowed from Medieval Latin algebra, from the Arabic الْجَبْر (al-jabr, “reunion, resetting of broken parts”) in the title of al-Khwarizmi's influential work الْكِتَاب الْمُخْتَصَر فِي حِسَاب الْجَبْر وَالْمُقَابَلَة (al-kitāb al-muḵtaṣar fī ḥisāb al-jabr wa-l-muqābala, “The Compendious Book on Calculation by Completion and Balancing”).

Meanings

  1. (uncountable) Elementary algebra: A system for representing and manipulating unknown quantities (variables) in equations.
    • Let us conceive, then, of an Algebra in which the symbols x, y, z, &c. admit indifferently of the values 0 and 1, and of these values alone. 1854, George Boole, “Signs and their Laws”, in An Investigation of the Laws of Thought, on which are Founded the Mathematical Theories of Logic and Probabilities, London: Walton and Maberly, page 37:
    • Also the rule of false position, with dyuers examples not only vulgar, but some appertaynyng to the rule of Algeber. 1551, James A.H. Murray, editor, A New English Dictionary on Historical Principles: Founded Mainly on the Materials Collected by the Philological Society., volume 1, Oxford: Clarendon Press, published 1888, Part 1, page 217:
  2. (capitalized, sometimes, uncountable) Abstract algebra: A broad field of study in modern mathematics (often mentioned alongside analysis) loosely characterized by its concern for abstraction and symmetry, dealing with the behavior, classification, and application of a large class of objects (called algebraic structures) and the maps between them (called, most generally, morphisms).
  3. (countable, uncountable) Any of several objects of study in Algebra ▸ A universal algebra.
  4. (countable, uncountable) Any of several objects of study in Algebra ▸ An algebraic structure consisting of a module over a commutative ring (or a vector space over a field) along with an additional binary operation that is bilinear over module (or vector) addition and scalar multiplication.
  5. (countable) A collection of subsets of a given set, such that this collection contains the empty set, and the collection is closed under unions and complements (and thereby also under intersections and differences).
  6. (countable, figuratively, uncountable) A system or process (especially one that is complex or convoluted) that substitutes one thing for another, or uses signs or symbols to represent concepts or ideas.
    • Fly ! Fly ! avaunt with that base cowardly gibbrish ; That Algebra of honour ; which had never Been nam'd, if all had equal courage—what? 1663, William Clark, edited by William Hugh Logan, Marciano; or, The discovery: A tragi-comedy, Edinburgh: Reprinted for Private Circulation, published 1871, →ISBN, page 13:
  7. (historical, rare, uncountable) The surgical treatment of a dislocated or fractured bone. Also (countable): a dislocation or fracture.
    • Algebra is used today by surgeons to mean bone-setting, i.e. the restoration of bones, and the idea of restoration is present in the mathematical context, too. 1987, John Newsome Crossley, “Latency”, in The emergence of number, Singapore: World Scientific, →ISBN, Al-Khwarizwi, page 65:
    • Ne take noon hede to brynge togidere þe parties of þe boon þat is to-broken or dislocate, til viij. daies ben goon in þe wyntir, & v. in þe somer; for þanne it schal make quytture, and be sikir from swellynge; & þanne brynge togidere þe brynkis eiþer þe disiuncture after þe techynge þat schal be seid in þe chapitle of algebra. a1420, The British Museum Additional MS, 12,056, “Wounds complicated by the Dislocation of a Bone”, in Robert von Fleischhacker, editor, Lanfranc's "Science of cirurgie.", London: K. Paul, Trench, Trübner & Co, translation of original by Lanfranc of Milan, published 1894, →ISBN, page 63:

Forms

SpellingFeaturesLabelsSource
algebras Number=Plur lexicographic

Deriveds

free algebra · algebroid · algebraism · bialgebra · Zinbiel algebra · superbialgebra · polynomial algebra · division algebra · algebralike · Grassmann algebra · Iwahori-Hecke algebra · non-associative algebra · Hurwitz algebra · algebraize · power-associative algebra · σ-algebra · Jordan algebra · Lie algebra · Abelian algebra · hyperalgebra · Azumaya algebra · Artin algebra · linear algebra · homological algebra · dialgebra · finite algebra · Weyl algebra · numerical linear algebra · switching algebra · simple algebra · Albert algebra · reduced algebra · k-algebra · abelian algebra · hard as Chinese algebra · free Boolean algebra · composition algebra · abstract algebra · Kac-Moody algebra · alternative algebra · Leibniz algebra · Hopf algebra · superalgebra · multialgebra · quaternion algebra · Clifford algebra · coalgebra · antialgebra · central simple algebra · Maharam algebra · algebraization · Boolean algebra · subalgebra · subalgebrae · Kleene algebra · prealgebra · universal algebra · F-algebra · Borel σ-algebra · algebra over a ring · shuffle algebra · algebra over a field · Heyting algebra · De Morgan algebra · matrix algebra · modern algebra · vector algebra · Hecke algebra · semialgebra · superdialgebra · associative algebra · commutative algebra · combinatorial commutative algebra · cogebra · algebraist · elementary algebra · algebrician · pseudoalgebra · quasibialgebra · submultialgebra · Banach algebra · Loday algebra · anti-algebra · Ockham algebra · sigma-algebra

Descendants

代数 · 代數

Hypernyms

ring

Hyponyms

σ-algebra

Relateds

algebraic · algebraically · algebraist · algebraical · algorithm

Synonyms

algebra of sets · algebra over a ring · field of sets · algebra over a field

Translations (148)

be а́лгебра (system for computation) · et algebra (system for computation) · gl álxebra (system for computation) · io algebro (system for computation) · de Algebra (system for computation) · pa ਬੀਜ ਗਣਿਤ (system for computation) · hi बीजगणित (system for computation) · vro algõbra (study of algebraic structures) · qu alhibra (study of algebraic structures) · kn ಬೀಜಗಣಿತ (system for computation) · ms aljabar (study of algebraic structures) · sv algebra (system for computation) · ms algebra (system for computation) · ru а́лгебра (study of algebraic structures) · tr cebir (system for computation) · hi बीजगणित (study of algebraic structures) · cmn 代數 /代数 (system for computation) · cs algebra (system for computation) · uk а́лгебра (study of algebraic structures) · ja 代数 (system for computation) · he אַלגֶבּרָה (system for computation) · et algebra (study of algebraic structures) · fr algèbre (system for computation) · gu બીજગણિત (system for computation) · ga ailgéabar (study of algebraic structures) · fa جبر (system for computation) · ka ალგებრა (system for computation) · ckb جەبر (system for computation) · da algebra (study of algebraic structures) · ur الجبرا (system for computation) · fr algèbre (structure) · fj ivakavakadina (study of algebraic structures) · or ବୀଜଗଣିତ (study of algebraic structures) · ro algebră (system for computation) · vi đại số học (study of algebraic structures) · ht aljèb (study of algebraic structures) · es álgebra (study of algebraic structures) · ast álxebra (system for computation) · scn àlgibbra (study of algebraic structures) · bg алгебра (set theory: collection of subsets) · nl algebra (system for computation) · ga ailgéabar (system for computation) · sk algebra (system for computation) · cs algebra (study of algebraic structures) · da algebra (system for computation) · sh алгебра (structure) · sq algjebër (system for computation) · ko 대수학 (study of algebraic structures) · az cəbr (system for computation) · fa جبر (study of algebraic structures) · ka ალგებრა (study of algebraic structures) · pl algebra (system for computation) · nl stelkunde (system for computation) · bg алгебра (structure) · es álgebra (structure) · ar جَبْر (system for computation) · or ବୀଜଗଣିତ (system for computation) · hy հանրահաշիվ (study of algebraic structures) · br lizherjedoniezh (system for computation) · is merkjamálsfræði (system for computation) · tl panandaan (system for computation) · fr algèbre (study of algebraic structures) · pl algebra (structure) · el άλγεβρα (study of algebraic structures) · kk алгебра (system for computation) · cmn 代數學 /代数学 (study of algebraic structures) · is merkjamálsfræði (study of algebraic structures) · it algebra (system for computation) · ja 多元環 (structure) · sh algebra (system for computation) · bg алгебра (one of several other types of mathematical structure) · ca àlgebra (system for computation) · el άλγεβρα (system for computation) · cs algebra (structure) · lv algebra (system for computation) · ko 대수 (system for computation) · yue 代數 /代数 (system for computation) · bg а́лгебра (study of algebraic structures) · et algebra (structure) · syc ܡܘܠܝܐ ܘܦܘܚܡܐ (system for computation) · ar عِلْم الْجَبْر (system for computation) · lt algebra (system for computation) · hy հանրահաշիվ (system for computation) · oc algèbra (system for computation) · sl algebra (system for computation) · mt alġebra (system for computation) · ja 代数学 (study of algebraic structures) · be а́лгебра (study of algebraic structures) · bo ཚབ་རྩིས (system for computation) · pt álgebra (structure) · hu algebra (study of algebraic structures) · id aljabar (system for computation) · yue 代數學 /代数学 (study of algebraic structures) · ru а́лгебра (system for computation) · no algebra (system for computation) · am አልጄብራ (system for computation) · ar عِلْم الْجَبْر (study of algebraic structures) · pt álgebra (study of algebraic structures) · ro algebră (study of algebraic structures) · es álgebra (system for computation) · mk алге́бра (system for computation) · km ពីជគណិត (system for computation) · fi algebra (one of several other types of mathematical structure) · af algebra (system for computation) · cmn 代數 /代数 (structure) · pa ਅਲਜਬਰਾ (system for computation) · fi algebra (system for computation) · sh algebra (structure) · iu ᑎᑎᖅᖃᑦ ᓈᓴᐅᑎᓐᖑᖅᑎᒋᐊᓖᑦ (study of algebraic structures) · ml ബീജഗണിതം (study of algebraic structures) · gv algeerey (study of algebraic structures) · tr cebir (study of algebraic structures) · nan-hbl 代數 /代数 (system for computation) · qu qillqanancha kamay (study of algebraic structures) · af algebra (structure) · af algebra (study of algebraic structures) · ms aljabar (system for computation) · ur الجبرا (study of algebraic structures) · ru а́лгебра (structure) · fi algebra (set theory: collection of subsets) · ms algebra (study of algebraic structures) · my အက္ခရာသင်္ချာ (system for computation) · sh алгебра (study of algebraic structures) · fi algebra (study of algebraic structures) · yi אַלגעברע (system for computation) · ml ബീജഗണിതം (system for computation) · sh алгебра (system for computation) · ar جَبْر (study of algebraic structures) · th พีชคณิต (system for computation) · sw aljebra (system for computation) · cy algebra (system for computation) · gd ailseabra (study of algebraic structures) · sq algjebër (study of algebraic structures) · sco algebra (system for computation) · ta இயற்கணிதம் (system for computation) · id ilmu hitung (system for computation) · fi algebra (structure) · mk алге́бра (study of algebraic structures) · pt álgebra (system for computation) · vi đại số (system for computation) · sh algebra (study of algebraic structures) · bn বীজগণিত (system for computation) · hu algebra (system for computation) · de Algebra (study of algebraic structures) · eo algebro (system for computation) · hu algebra (structure) · pl algebra (study of algebraic structures) · mk алге́бра (structure)

wikidata: Q3968 · wikipedia: al-Khwarizmi