Definition of algebra in English:



  • 1[mass noun] The 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’
    • ‘Pierre went on to study the latest mathematics, in particular studying algebra and geometry.’
    • ‘We have looked briefly at Zorn's contributions to algebra and to set theory.’
    • ‘König worked on a wide range of topics in algebra, number theory, geometry, set theory, and analysis.’
    • ‘Ernst Schröder's important work is in the area of algebra, set theory and logic.’
    • ‘He failed in his application for the chair of algebra and number theory at Uppsala University.’
    • ‘He wrote several books on arithmetic, algebra, geometry and astronomy.’
    • ‘It was an exciting time with increasing mathematical activity in algebra.’
    • ‘The mathematical topics that Delone studied include algebra, the geometry of numbers.’
    • ‘He worked on algebra and graph theory, combining the two to produce his first outstanding contribution to matroid theory.’
    • ‘It is time to take a look at this most outstanding work on algebra in Greek mathematics.’
    • ‘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.’
    • ‘He had a distinguished career as a math professor, specializing in algebra, algebraic geometry and number theory.’
    • ‘I do not doubt that this is the most important work on general algebra that the Annalen has ever published.’
    • ‘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.’
    • ‘Wall's research is mostly in the area of geometric topology and related algebra.’
    • ‘Aitken's mathematical work was in statistics, numerical analysis, and algebra.’
    • ‘Among his many mathematical achievements can be included profound discoveries in logic, algebra and differential equations.’
    • ‘Mill only deals with geometry, arithmetic, and some algebra, not the branches of higher mathematics.’
    1. 1.1 A system of algebra based on given axioms.
      • ‘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.’
      • ‘Malcev also studied Lie groups and topological algebras, producing a synthesis of algebra and mathematical logic.’
      • ‘The very next year the note ‘Subsumption of Boolean algebras under the theory of rings’ appeared in the same journal.’
      • ‘Wedderburn made important advances in the theory of rings, algebras and matrix theory.’
      • ‘Dickson worked on finite fields and extended the theory of linear associative algebras initiated by Wedderburn and Cartan.’
      • ‘On the web, there are pages on counterexamples in functional analysis, Clifford algebras, and mathematical programming.’
      • ‘He also published results on algebras which were fundamental in the study of algebraic number fields.’
      • ‘His mathematical publications started in 1964 with a series of papers on topological algebras, measure algebras and Banach algebras.’
      • ‘Topology, cohomology, Lie algebras, and knot theory have all become valuable items in the physicist's tool chest.’
      • ‘In 1870 Peirce published, at his own expense, Linear Associative Algebra a classification of all complex associative algebras of dimension less than seven.’
      • ‘Even for propositional logics, models of such systems are usually algebras, e.g., Boolean or Heyting algebras, and as such they are categories.’
      • ‘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.’
      • ‘He had been responsible for major advances in the theory of finite dimensional algebras and was the discoverer of modular representation theory.’
      • ‘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.’
      • ‘Jordan algebras are called after the German physicist and mathematician Pascual Jordan.’
      • ‘The theorem states that all central division algebras over algebraic number fields are cyclic algebras.’
      • ‘He studied algebras and published papers on trigonometrical series.’
      • ‘This was the time when Brauer made his fundamental contribution to the algebraic theory of simple algebras.…’


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).