Definition of algebraic in English:



  • 1Relating to or involving algebra.

    • ‘Betti extended and gave proofs relating to the algebraic concepts of Galois theory.’
    • ‘Does Rijndael's algebraic formulation make the algorithm easier to crack than other cryptosystems not designed this way?’
    • ‘This gave powerful results such as a purely algebraic proof of the Riemann Roch theorem.’
    • ‘In other work he looked at problems relating properties of algebraic number fields to algebraic K-theory.’
    • ‘Bromwich also made useful contributions to quadratic and bilinear forms and many consider his algebraic work to be his finest.’
    • ‘He tried, with great success, to show why the introduction of algebraic notation was necessary and inevitable.’
    • ‘It also meant that Wiles' earlier work in algebraic number theory would be helpful, and that he would probably generate some interesting problems-whether or not he found a proof.’
    • ‘Albanese's research involved examining curves on algebraic surfaces and the genus of an algebraic variety.’
    • ‘It dealt with the sum of integrals of a given algebraic function.’
    • ‘Baker, while on a visit to Göttingen, was inspired by Klein to study algebraic function theory.’
    • ‘Back in Berlin he worked on his doctoral thesis on algebraic number theory under Dirichlet's supervision.’
    • ‘The papers look at algebraic curves, the Riemann Roch theorem and algebraic polynomials.’
    • ‘Even his analytical work was guided by algebraic and linear algebraic methods.’
    • ‘According to Rotman, the justification of homological algebra is that it eventually proved useful in solving purely algebraic problems.’
    • ‘Fermat preferred the algebraic techniques that he used to such devastating effect in number theory.’
    • ‘Remak made important contributions to algebraic number theory.’
    • ‘In 1874 he submitted this doctoral dissertation on algebraic integers and was awarded the degree.’
    • ‘Herbrand also worked on field theory considering abelian extensions of algebraic number fields.’
    • ‘He also published results on algebras which were fundamental in the study of algebraic number fields.’
    • ‘His work in algebraic number theory led him to study the quaternions and generalisations such as Clifford algebras.’
    1. 1.1Denoting a mathematical expression or equation in which a finite number of symbols are combined using only the operations of addition, subtraction, multiplication, division, and exponentiation with constant rational exponents.
      Compare with transcendental
      • ‘The OR gates and AND gates you can read about in books that describe how computers work correspond directly to Boole's algebraic operations of addition and multiplication.’
      • ‘Over the years, mathematicians have developed a variety of such invariants, often expressed in the form of a polynomial algebraic expression.’
      • ‘These books allowed new generations of mathematicians to learn algebraic topology and homological algebra directly in the categorical language and to master the method of diagrams.’
      • ‘His research interests include topology, algebraic geometry, and Lie theory.’
      • ‘They can solve a variety of two-step problems using variables, identify equivalent algebraic expressions, and solve linear equations and inequalities.’
      • ‘In this book, Boole showed how to apply ordinary algebra to human thought processes, writing down algebraic equations in which the unknowns denoted not numbers but human thoughts.’
      • ‘After writing a thesis on algebraic functions and equations, he worked on space curves.’
      • ‘Few have had the simultaneous grasp of topology, algebraic geometry and K-theory that Thomason did.’
      • ‘Arabic mathematicians learned to manipulate polynomials, to solve certain algebraic equations, and more.’
      • ‘Omar Khayyam, known chiefly in Europe as a poet, combined trigonometry and approximation theory to solve algebraic equations using geometry.’
      • ‘Naimark's first work for his candidate's thesis was on the separation of roots of algebraic equations.’
      • ‘Paniker not only played upon the abstraction of the words and scripts but also incorporated mathematical formulae, algebraic equations and diagrams of horoscopes.’
      • ‘To do this, he advanced the study of differential equations from numbers, formulas, and the manipulation of algebraic equations to geometry, curves, and the visualization of flows.’
      • ‘The main innovation was Playfair's use of algebraic notation to abbreviate the proofs which he taught in his class.’
      • ‘His arithmetic setting of this result led eventually to the modern abstract theory of algebraic functions.’
      • ‘In his lectures Sylow explained Abel's and Galois's work on algebraic equations.’
      • ‘Since we know that this distance is 260 miles, we can write the following algebraic equation to represent this information.’
      • ‘It has proved to be the computational method of choice for symbolic manipulation in algebraic geometry, differential equations, and combinatorics.’
      • ‘Her mother always reminded her of how she was doing long division when she was three and complex algebraic equations by the time she was five.’
      • ‘Vedic mathematics, which simplifies arithmetic and algebraic operations, has increasingly found acceptance the world over.’