# algebra
## English
### Etymology

Borrowed from Medieval Latin algebra, from the Arabic word 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”).

### Pronunciation

* (UK) IPA: /ˈæl.dʒɪ.bɹə/
* (US) IPA: /ˈæl.d͡ʒɪ.bɹə/, /ˈæl.d͡ʒə.bɹə/
* Audio (US):(file)

### Noun

algebra (countable and uncountable, plural algebras)
* (uncountable, mathematics) Elementary algebra: A system for representing and manipulating unknown quantities (variables) in equations.
** 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:Also the rule of false position, with dyuers examples not only vulgar, but some appertaynyng to the rule of Algeber.
** 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: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.
* (uncountable, mathematics, sometimes capitalized) 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).
* (countable, mathematics, algebra) Any of several objects of study in Algebra
** A universal 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.
    Synonyms: algebra over a field, algebra over a ring
* (countable, set theory, mathematical analysis) 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).
    Synonyms: field of sets, algebra of sets
    Hypernym: ring
    Hyponym: σ-algebra
* (figurative) 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.
** 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:Fly ! Fly ! avaunt with that base cowardly gibbrish ; That Algebra of honour ; which had never Been nam'd, if all had equal courage—what?
* (uncountable, medicine, historical, rare) The surgical treatment of a dislocated or fractured bone. Also (countable): a dislocation or fracture.
** 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: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.
** 1987, John Newsome Crossley, “Latency”, in The emergence of number‎, Singapore: World Scientific, →ISBN, Al-Khwarizwi, page 65: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.

#### Derived terms

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

#### Related terms

* algebraic
* algebraical
* algebraically
* algebraist
* algorithm

#### Translations
### Anagrams

* Labarge

## Czech
### Etymology

Borrowed from Arabic الْجَبْر (al-jabr, “reunion, resetting of broken parts”); see also the English algebra.

### Pronunciation

* IPA: [ˈalɡɛbra]

### Noun

algebra f
* algebra

#### Derived terms

* Booleova algebra
* booleovská algebra

#### Related terms

* algebraický

### Further reading

* “algebra”, in Příruční slovník jazyka českého (in Czech), 1935–1957
* “algebra”, in Slovník spisovného jazyka českého (in Czech), 1960–1971, 1989

## Danish
### Etymology

Borrowed from Medieval Latin algebra, from Arabic الْجَبْر (al-jabr).

### Noun

algebra c (singular definite algebraen, not used in plural form)
* (mathematics) algebra (using symbols)
* (mathematics) algebra (study of algebraical structures)

#### Declension
## Dutch
### Etymology

From Middle Dutch algebra, from Latin algebra, from Arabic الْجَبْر (al-jabr).

### Pronunciation

* IPA: /ˈɑl.ɣəˌbraː/
* Audio:(file)
* Hyphenation: al‧ge‧bra

### Noun

algebra f (uncountable)
* (mathematics) algebra
    Synonyms: stelkunde, stelkunst

#### Derived terms

* algebraïcus
* algebraïsch
* algebraïst
* lineaire algebra

## Finnish
### Etymology

From New Latin algebra, from Arabic الْجَبْر (al-jabr).

### Pronunciation

* IPA: /ˈɑlɡebrɑ/, [ˈɑ̝lɡe̞brɑ̝]
* Rhymes: -ɑlɡebrɑ
* Hyphenation: al‧geb‧ra

### Noun

algebra
* algebra

#### Declension

Possessive forms of algebra (Kotus type 11/omena, no gradation) :
first-person singular possessor
singular
plural
nominative
algebrani
algebrani
accusative
nom.
algebrani
algebrani
gen.
algebrani
genitive
algebrani
algebrieni algebroideni algebroitteni algebrojeni $^{rare}$ algebraini $^{rare}$
partitive
algebraani
algebriani algebroitani algebrojani $^{rare}$
inessive
algebrassani
algebroissani algebrissani
elative
algebrastani
algebroistani algebristani
illative
algebraani
algebriini algebroihini
adessive
algebrallani
algebroillani algebrillani
ablative
algebraltani
algebroiltani algebriltani
allative
algebralleni
algebroilleni algebrilleni
essive
algebranani
algebroinani algebrinani
translative
algebrakseni
algebroikseni algebrikseni
abessive
algebrattani
algebroittani algebrittani
instructive
comitative
—algebroineni algebrineni
second-person singular possessor
singular
plural
nominative
algebrasi
algebrasi
accusative
nom.
algebrasi
algebrasi
gen.
algebrasi
genitive
algebrasi
algebriesi algebroidesi algebroittesi algebrojesi $^{rare}$ algebraisi $^{rare}$
partitive
algebraasi
algebriasi algebroitasi algebrojasi $^{rare}$
inessive
algebrassasi
algebroissasi algebrissasi
elative
algebrastasi
algebroistasi algebristasi
illative
algebraasi
algebriisi algebroihisi
adessive
algebrallasi
algebroillasi algebrillasi
ablative
algebraltasi
algebroiltasi algebriltasi
allative
algebrallesi
algebroillesi algebrillesi
essive
algebranasi
algebroinasi algebrinasi
translative
algebraksesi
algebroiksesi algebriksesi
abessive
algebrattasi
algebroittasi algebrittasi
instructive
comitative
—algebroinesi algebrinesi
first-person plural possessor
singular
plural
nominative
algebramme
algebramme
accusative
nom.
algebramme
algebramme
gen.
algebramme
genitive
algebramme
algebriemme algebroidemme algebroittemme algebrojemme $^{rare}$ algebraimme $^{rare}$
partitive
algebraamme
algebriamme algebroitamme algebrojamme $^{rare}$
inessive
algebrassamme
algebroissamme algebrissamme
elative
algebrastamme
algebroistamme algebristamme
illative
algebraamme
algebriimme algebroihimme
adessive
algebrallamme
algebroillamme algebrillamme
ablative
algebraltamme
algebroiltamme algebriltamme
allative
algebrallemme
algebroillemme algebrillemme
essive
algebranamme
algebroinamme algebrinamme
translative
algebraksemme
algebroiksemme algebriksemme
abessive
algebrattamme
algebroittamme algebrittamme
instructive
comitative
—algebroinemme algebrinemme
second-person plural possessor
singular
plural
nominative
algebranne
algebranne
accusative
nom.
algebranne
algebranne
gen.
algebranne
genitive
algebranne
algebrienne algebroidenne algebroittenne algebrojenne $^{rare}$ algebrainne $^{rare}$
partitive
algebraanne
algebrianne algebroitanne algebrojanne $^{rare}$
inessive
algebrassanne
algebroissanne algebrissanne
elative
algebrastanne
algebroistanne algebristanne
illative
algebraanne
algebriinne algebroihinne
adessive
algebrallanne
algebroillanne algebrillanne
ablative
algebraltanne
algebroiltanne algebriltanne
allative
algebrallenne
algebroillenne algebrillenne
essive
algebrananne
algebroinanne algebrinanne
translative
algebraksenne
algebroiksenne algebriksenne
abessive
algebrattanne
algebroittanne algebrittanne
instructive
comitative
—algebroinenne algebrinenne
third-person possessor
singular
plural
nominative
algebransa
algebransa
accusative
nom.
algebransa
algebransa
gen.
algebransa
genitive
algebransa
algebriensa algebroidensa algebroittensa algebrojensa $^{rare}$ algebrainsa $^{rare}$
partitive
algebraansa
algebriaan algebroitaan algebriansa algebroitansa algebrojaan $^{rare}$ algebrojansa $^{rare}$
inessive
algebrassaan algebrassansa
algebroissaan algebrissaan algebroissansa algebrissansa
elative
algebrastaan algebrastansa
algebroistaan algebristaan algebroistansa algebristansa
illative
algebraansa
algebriinsa algebroihinsa
adessive
algebrallaan algebrallansa
algebroillaan algebrillaan algebroillansa algebrillansa
ablative
algebraltaan algebraltansa
algebroiltaan algebriltaan algebroiltansa algebriltansa
allative
algebralleen algebrallensa
algebroilleen algebrilleen algebroillensa algebrillensa
essive
algebranaan algebranansa
algebroinaan algebrinaan algebroinansa algebrinansa
translative
algebrakseen algebraksensa
algebroikseen algebrikseen algebroiksensa algebriksensa
abessive
algebrattaan algebrattansa
algebroittaan algebrittaan algebroittansa algebrittansa
instructive
comitative
—algebroineen algebrineen algebroinensa algebrinensa :

#### Derived terms

* algebrallinen
* alkeisalgebra
* joukkoalgebra
* lineaarialgebra
* matriisialgebra
* relaatioalgebra
* universaalialgebra
* vektorialgebra

### Further reading

* “algebra”, in Kielitoimiston sanakirja [Dictionary of Contemporary Finnish]‎ (in Finnish) (online dictionary, continuously updated), Kotimaisten kielten keskuksen verkkojulkaisuja 35, Helsinki: Kotimaisten kielten tutkimuskeskus (Institute for the Languages of Finland), 2004–, retrieved 2023-07-02

## Hungarian
### Etymology

From Latin algebra, from Arabic الْجَبْر (al-jabr).

### Pronunciation

* IPA: [ˈɒlɡɛbrɒ]
* Hyphenation: al‧geb‧ra
* Rhymes: -rɒ

### Noun

algebra
* (mathematics) algebra (a system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols)
* (education) algebra (the study of algebra as a school subject)
    Tudnál segíteni algebrában? ― Could you help me with my algebra?

#### Derived terms

* algebrai

### References

* ↑ Tótfalusi, István. Idegenszó-tár: Idegen szavak értelmező és etimológiai szótára (’A Storehouse of Foreign Words: an explanatory and etymological dictionary of foreign words’). Budapest: Tinta Könyvkiadó, 2005. →ISBN

### Further reading

* algebra in Bárczi, Géza and László Országh. A magyar nyelv értelmező szótára (“The Explanatory Dictionary of the Hungarian Language”, abbr.: ÉrtSz.). Budapest: Akadémiai Kiadó, 1959–1962. Fifth ed., 1992: →ISBN
* algebra in Nóra Ittzés, editor, A magyar nyelv nagyszótára [A Comprehensive Dictionary of the Hungarian Language] (Nszt.), Budapest: Akadémiai Kiadó, 2006–2031 (work in progress; published a–ez as of 2024).

## Italian
### Etymology

From Medieval Latin algebra, from Arabic الْجَبْر (al-jabr, “reunion, resetting of broken parts”).

### Pronunciation

* IPA: /ˈal.d͡ʒe.bra/
* Rhymes: -aldʒebra
* Hyphenation: àl‧ge‧bra

### Noun

algebra f (plural algebre)
* algebra

#### Related terms

* algebrico
* algebrista

### Anagrams

* alberga

## Latin
### Etymology

Borrowed from Arabic الْجَبْر (al-jabr, “reunion, resetting of broken parts”).

### Pronunciation

* (Classical Latin) IPA: /ˈal.ɡe.bra/, [ˈäɫ̪ɡɛbrä]
* (modern Italianate Ecclesiastical) IPA: /ˈal.d͡ʒe.bra/, [ˈäl̠ʲd͡ʒebrä]

### Noun

algebra f (genitive algebrae); first declension
* (Medieval Latin, New Latin) algebra

#### Declension

First-declension noun.

### References

* algebra in Charles du Fresne du Cange’s Glossarium Mediæ et Infimæ Latinitatis (augmented edition with additions by D. P. Carpenterius, Adelungius and others, edited by Léopold Favre, 1883–1887)

## Latvian
### Etymology

Via other European languages, ultimately from Medieval Latin algebra, from Arabic الْجَبْر (al-jabr, “reunion, resetting of broken parts”) in the title of al-Khwarizmi's influential work الْكِتَاب الْمُخْتَصَر فِي حِسَاب اَلْجَبْر وَالْمُقَابَلَة (al-kitāb al-muḵtaṣar fī ḥisāb al-jabr wa-l-muqābala, “The Compendious Book on Calculation by Completion and Balancing”).

### Pronunciation

* IPA: [alɡɛbɾa]
* Audio:(file)

### Noun

algebra f (4th declension)
* algebra is a branch of mathematics that studies generic numbers ('variables') regardless of their actual numeric value; the corresponding school subject
    algebras formula ― algebraic formula
    algebras specialists ― algebra specialist
    algebras mācību grāmata ― algebra textbook
    algebras stunda ― algebra class, lesson
    risināt, atrisināt algebras uzdevumu ― to solve an algebra problem
    algebra ir viena no matematikas pamatnozarēm ― algebra is one of the fundamental branches of mathematics

#### Derived terms

* algebrisks

## Norwegian Bokmål
### Etymology

From Arabic الْجَبْر (al-jabr), via Medieval Latin algebra.

### Noun

algebra m (definite singular algebraen, indefinite plural algebraer, definite plural algebraene)
* (mathematics) algebra
* an algebra textbook

#### Derived terms

* algebraisk
* lineær algebra

### References

* “algebra” in The Bokmål Dictionary.

## Norwegian Nynorsk
### Etymology

From Arabic الْجَبْر (al-jabr), via Medieval Latin algebra.

### Noun

algebra m (definite singular algebraen, indefinite plural algebraer, definite plural algebraene)
* (mathematics) algebra
* an algebra textbook

#### Derived terms

* algebraisk
* lineær algebra

### References

* “algebra” in The Nynorsk Dictionary.

## Polish
### Etymology

Internationalism; compare English algebra. Possibly borrowed from German Algebra, French algèbre, or Spanish álgebra, ultimately from Medieval Latin algebra, from Arabic الْجَبْر (al-jabr) “reunion”, “resetting of broken parts”, used 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 restoration and equating like with like”). First attested in 1654–1676.

### Pronunciation

* IPA: /alˈɡɛ.bra/
* Audio:(file)
* Rhymes: -ɛbra
* Syllabification: al‧ge‧bra

### Noun

algebra f
* algebra (field of mathematics)

#### Derived terms

* algebraiczny
* algebraicznie
* algebra abstrakcyjna
* algebraik

#### Collocations

* uogólniona algebra ― generalized algebra
* matematyczna algebra ― mathematical algebra
* klasyczna algebra ― classic(al) algebra
* współczesna algebra ― modern algebra
* prosta algebra ― simple algebra
* zwykła algebra ― ordinary algebra
* algebra liniowa ― linear algebra
* algebra homologiczna ― homological algebra
* algebra abstrakcyjna ― algebra
* algebra przemienna ― commutative algebra
* algebra geometryczna ― geometric algebra
* algebra uniwersalna ― universal algebra
* algebra komputerowa ― computational algebra
* algebra ogólna ― general algebra
* algebra liczbowa ― numerical algebra
* algebra wyższa ― higher-level algebra
* algebra elementarna ― elementary algebra
* algebra centralna prosta ― central simple algebra
* algebra łączna ― associative algebra
* algebra prosta ― simple algebra
* homomorfizm algebry ― homomorphism of algebra
* operatory algebry ― algebra operators
* twierdzenie algebry ― theorum/statement of algebra
* podręcznik algebry ― an algebra textbook
* teoria algebr ― theory of algebras
* wykładowca algebry ― an algebra instructor
* dział/zakład algebry ― the branch of algebra
* język algebry ― the language of algebra
* reprezentacja algebry ― representation of algebra
* nauczyciel algebry ― an algebra teacher
* podstawy algebry ― the basics of algebra
* zasady algebry ― the rules of algebra
* metody algebry ― methods of algebra
* system algebry ― system of algebra
* dziedzina algebry ― field of algebra
* konstrukcja algebry ― construction of algebra
* badania algebry ― algebra research
* rozwój algebry ― development algebra
* prawa algebry ― laws of algebra
* algebra Clifforda ― Clifford algebra
* algebra Liego ― Lie algebra
* algebra Bool-skiego/Boole'a/Boola ― Boolean algebra
* algebra Banacha ― Banach algebra
* algebra kwaternionów ― algebra of quaternions
* algebra termów ― algebra of terms
* algebra macierzy ― algebra of matrices
* algebra zbiorów ― algebra of sets
* algebra operatorów ― algebra of operators
* algebra liczb ― algebra of numbers
* algebra relacji ― algebra of relations
* używać algebry ― to use algebra
* uczyć algebry ― to teach algebra
* uczyć się algebry ― to learn algebra
* tworzyć algebrę ― to create algebra

### References

* ↑ Mirosław Bańko, Lidia Wiśniakowska (2021) “algebra”, in Wielki słownik wyrazów obcych, →ISBN
* ↑ Bańkowski, Andrzej (2000) “algebra”, in Etymologiczny słownik języka polskiego [Etymological Dictionary of the Polish Language] (in Polish)
* ↑ Barbara Rykiel-Kempf (06.05.2009) “ALGEBRA”, in Elektroniczny Słownik Języka Polskiego XVII i XVIII Wieku [Electronic Dictionary of the Polish Language of the XVII and XVIII Century]

### Further reading

* algebra in Wielki słownik języka polskiego, Instytut Języka Polskiego PAN
* algebra in Polish dictionaries at PWN
* Samuel Bogumił Linde (1807–1814) “algiebra”, in Słownik języka polskiego
* Aleksander Zdanowicz (1861) “algiebra”, in Słownik języka polskiego, Wilno 1861
* J. Karłowicz, A. Kryński, W. Niedźwiedzki, editors (1900), “algiebra”, in Słownik języka polskiego (in Polish), volume 1, Warsaw, page 24

## Serbo-Croatian
### Pronunciation

* IPA: /ǎlɡeːbra/
* Hyphenation: al‧ge‧bra

### Noun

àlgēbra f (Cyrillic spelling а̀лге̄бра)
* algebra

#### Declension
### Further reading

* “algebra”, in Hrvatski jezični portal [Croatian language portal] (in Serbo-Croatian), 2006–2025

## Spanish
### Noun

algebra
* Misspelling of álgebra.

## Swedish
### Noun

algebra c
* (mathematics) algebra

#### Declension

| | | nominative | genitive |
| singular | indefinite | algebra | algebras |
| singular | definite | algebran | algebrans |
| plural | indefinite | algebror | algebrors |
| plural | definite | algebrorna | algebrornas |

#### Related terms

* algebraisk
* relationsalgebra

## Welsh
### Noun

algebra m or f (uncountable)
* (mathematics) algebra
    Synonym: (obsolete) alsoddeg

#### Mutation

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

### References

* Delyth Prys, J.P.M. Jones, Owain Davies, Gruffudd Prys (2006) Y Termiadur: termau wedi'u safoni; standardised terminology‎ (in Welsh), Cardiff: Awdurdod cymwysterau, cwricwlwm ac asesu Cymru (Qualifications curriculum & assessment authority for Wales), →ISBN
* R. J. Thomas, G. A. Bevan, P. J. Donovan, A. Hawke et al., editors (1950–present), “algebra”, in Geiriadur Prifysgol Cymru Online (in Welsh), University of Wales Centre for Advanced Welsh & Celtic Studies