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
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 (redirect from Artin-Schreier extension)
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
Picard–Vessiot theory (redirect from Picard-Vessiot extension)
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
Semiabelian group (redirect from Semiabelian group (Galois theory))
(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