• significance of being a Galois extension is that the extension has a Galois group and obeys the fundamental theorem of Galois theory. A result of Emil...
    8 KB (1,100 words) - 22:29, 3 May 2024
  • Thumbnail for Galois theory
    In mathematics, Galois theory, originally introduced by Évariste Galois, provides a connection between field theory and group theory. This connection...
    32 KB (4,192 words) - 06:56, 26 June 2024
  • In mathematics, a Galois module is a G-module, with G being the Galois group of some extension of fields. The term Galois representation is frequently...
    15 KB (1,927 words) - 19:44, 5 August 2024
  • group the Galois group of a Galois extension of the rational numbers? (more unsolved problems in mathematics) In Galois theory, the inverse Galois problem...
    16 KB (2,529 words) - 23:58, 22 November 2023
  • Galois theory is parallel to algebraic Galois theory. One difference between the two constructions is that the Galois groups in differential Galois theory...
    12 KB (1,627 words) - 14:44, 9 September 2024
  • In mathematics, Grothendieck's Galois theory is an abstract approach to the Galois theory of fields, developed around 1960 to provide a way to study the...
    4 KB (569 words) - 23:59, 12 February 2024
  • Artin–Schreier theory is a branch of Galois theory, specifically a positive characteristic analogue of Kummer theory, for Galois extensions of degree equal to the characteristic...
    3 KB (466 words) - 16:54, 3 November 2021
  • Finite field (redirect from Galois field)
    In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any...
    45 KB (6,162 words) - 13:35, 7 August 2024
  • differential field extension generated by the solutions of a linear differential equation, using the differential Galois group of the field extension. A major goal...
    8 KB (898 words) - 00:09, 18 August 2023
  • (1984) and named by Matzat (1987). It appears in Galois theory, in the study of the inverse Galois problem or the embedding problem which is a generalization...
    8 KB (912 words) - 12:41, 2 February 2024