algebra
Language: English
Part of speech: noun
Pronunciation: ipa: /ˈæl.dʒɪ.bɹə/
ipa: /ˈæl.d͡ʒɪ.bɹə/
ipa: /ˈæl.d͡ʒə.bɹə/
note: Indic
ipa: /əlˈdʒibra/
Forms: form: algebras
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”).
Senses: examples: text: Also the rule of false position, with dyuers examples not only vulgar, but some appertaynyng to the rule of Algeber.
ref: 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:
text: 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.
ref: 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:
topics: mathematics
sciences
glosses: Elementary algebra: A system for representing and manipulating unknown quantities (variables) in equations.
topics: mathematics
sciences
glosses: 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).
topics: algebra
mathematics
sciences
glosses: Any of several objects of study in Algebra
A universal algebra.
topics: algebra
mathematics
sciences
glosses: 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.
synonyms: algebra over a field
algebra over a ring
topics: mathematical-analysis
mathematics
sciences
set-theory
synonyms: field of sets
algebra of sets
hypernyms: ring
hyponyms: σ-algebra
glosses: 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).
examples: text: Fly ! Fly ! avaunt with that base cowardly gibbrish ; That Algebra of honour ; which had never Been nam'd, if all had equal courage—what?
ref: 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:
glosses: 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.
examples: text: 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.
ref: 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:
text: 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.
ref: 1987, John Newsome Crossley, “Latency”, in The emergence of number, Singapore: World Scientific, →ISBN, Al-Khwarizwi, page 65:
topics: medicine
sciences
glosses: The surgical treatment of a dislocated or fractured bone. Also (countable): a dislocation or fracture.
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
sigma-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