Definition of "algebra"

algebra

/ˈæl.dʒɪ.bɹə/

noun
countable and uncountable, plural algebras
1. (uncountable, mathematics) Elementary algebra: A system for representing and manipulating unknown quantities (variables) in equations.
  Quotations
  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
  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
2. (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).
3. (countable, mathematics, algebra) Any of several objects of study in Algebra
  1. A universal algebra.
  2. 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.
    Quotations
    In mathematics, a Lie algebra (pronounced /liː/ "Lee") is a vector space g {\displaystyle {\mathfrak {g}}} together with a non-associative, alternating bilinear map g × g → g ; ( x , y ) ↦ [ x , y ] {\displaystyle {\mathfrak {g}}\times {\mathfrak {g}}\rightarrow {\mathfrak {g}};(x,y)\mapsto [x,y]} , called the Lie bracket, satisfying the Jacobi identity.
    2018 March 23, Wikipedia contributors, “Lie algebra”, in English Wikipedia‎, Wikimedia Foundation, revision 831953572
4. (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).
5. (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.
  Quotations
  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, page 13
6. (uncountable, medicine, historical, rare) The surgical treatment of a dislocated or fractured bone. Also (countable): a dislocation or fracture.
  Quotations
  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, page 63
  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, Al-Khwarizwi, page 65

Definition of "algebra"

algebra

noun

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