Definition of algebra in English:


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  • 1The part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.

    ‘courses in algebra, geometry, and Newtonian physics’
    • ‘Among his many mathematical achievements can be included profound discoveries in logic, algebra and differential equations.’
    • ‘Aitken's mathematical work was in statistics, numerical analysis, and algebra.’
    • ‘König worked on a wide range of topics in algebra, number theory, geometry, set theory, and analysis.’
    • ‘He worked on algebra and graph theory, combining the two to produce his first outstanding contribution to matroid theory.’
    • ‘He had a distinguished career as a math professor, specializing in algebra, algebraic geometry and number theory.’
    • ‘It was an exciting time with increasing mathematical activity in algebra.’
    • ‘It is time to take a look at this most outstanding work on algebra in Greek mathematics.’
    • ‘He wrote several books on arithmetic, algebra, geometry and astronomy.’
    • ‘Mill only deals with geometry, arithmetic, and some algebra, not the branches of higher mathematics.’
    • ‘Ernst Schröder's important work is in the area of algebra, set theory and logic.’
    • ‘The mathematical topics that Delone studied include algebra, the geometry of numbers.’
    • ‘I do not doubt that this is the most important work on general algebra that the Annalen has ever published.’
    • ‘The book contained the elements of geometry and algebra in addition to the calculus.’
    • ‘In short, his interest in classical algebra and number theory brought him to abstract semigroups.’
    • ‘We have looked briefly at Zorn's contributions to algebra and to set theory.’
    • ‘Pierre went on to study the latest mathematics, in particular studying algebra and geometry.’
    • ‘He failed in his application for the chair of algebra and number theory at Uppsala University.’
    • ‘Wall's research is mostly in the area of geometric topology and related algebra.’
    • ‘They are the basis of mathematical logic, which in turn gives rise to Boolean algebra.’
    • ‘It is devoted mainly to arithmetic and algebra, with just a few problems on geometry and mensuration.’
    1. 1.1A system of algebra based on given axioms.
      ‘This was the time when Brauer made his fundamental contribution to the algebraic theory of simple algebras.…’
      • ‘Malcev also studied Lie groups and topological algebras, producing a synthesis of algebra and mathematical logic.’
      • ‘In 1870 Peirce published, at his own expense, Linear Associative Algebra a classification of all complex associative algebras of dimension less than seven.’
      • ‘Topology, cohomology, Lie algebras, and knot theory have all become valuable items in the physicist's tool chest.’
      • ‘His mathematical publications started in 1964 with a series of papers on topological algebras, measure algebras and Banach algebras.’
      • ‘The theorem states that all central division algebras over algebraic number fields are cyclic algebras.’
      • ‘Dickson worked on finite fields and extended the theory of linear associative algebras initiated by Wedderburn and Cartan.’
      • ‘Even for propositional logics, models of such systems are usually algebras, e.g., Boolean or Heyting algebras, and as such they are categories.’
      • ‘He had been responsible for major advances in the theory of finite dimensional algebras and was the discoverer of modular representation theory.’
      • ‘The very next year the note ‘Subsumption of Boolean algebras under the theory of rings’ appeared in the same journal.’
      • ‘He also made very substantial contributions to nonassociative algebras, in particular Lie algebras and Jordan algebras.’
      • ‘In 1984 Jones discovered an astonishing relationship between von Neumann algebras and geometric topology.’
      • ‘It completes the formation of the theory of free associative algebras and related classes of rings as an independent domain of ring theory.’
      • ‘In 1923 he published important work on real and complex algebras of low dimension.’
      • ‘Wedderburn made important advances in the theory of rings, algebras and matrix theory.’
      • ‘He also published results on algebras which were fundamental in the study of algebraic number fields.’
      • ‘He studied algebras and published papers on trigonometrical series.’
      • ‘They made plans to write a joint paper on splitting fields of division algebras, which was to contain an example showing that the degree of a minimal splitting field can be arbitrarily large.’
      • ‘On the web, there are pages on counterexamples in functional analysis, Clifford algebras, and mathematical programming.’
      • ‘Jordan algebras are called after the German physicist and mathematician Pascual Jordan.’



/ˈaljəbrə/ /ˈældʒəbrə/


Late Middle English from Italian, Spanish, and medieval Latin, from Arabic al-jabr ‘the reunion of broken parts’, ‘bone-setting’, from jabara ‘reunite, restore’. The original sense, ‘the surgical treatment of fractures’, probably came via Spanish, in which it survives; the mathematical sense comes from the title of a book, ‘ilm al-jabr wa'l-muqābala ‘the science of restoring what is missing and equating like with like’, by the mathematician al-Ḵwārizmī (see algorithm).