area of abstract algebra known as Galois theory, the Galois group of a certain type of field extension is a specific group associated with the field extension...
18 KB (3,190 words) - 20:36, 19 July 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
release from prison, Galois fought in a duel and died of the wounds he suffered. Galois was born on 25 October 1811 to Nicolas-Gabriel Galois and Adélaïde-Marie...
41 KB (4,795 words) - 17:05, 17 August 2024
absolute Galois group GK of a field K is the Galois group of Ksep over K, where Ksep is a separable closure of K. Alternatively it is the group of all automorphisms...
7 KB (905 words) - 11:11, 24 April 2024
development of Galois theory. In its most basic form, the theorem asserts that given a field extension E/F that is finite and Galois, there is a one-to-one...
16 KB (2,775 words) - 17:26, 20 December 2023
and roots similar to the formula above. Modern Galois theory generalizes the above type of Galois groups by shifting to field theory and considering field...
101 KB (13,126 words) - 14:06, 5 August 2024
automorphism group Aut(E/F) is precisely the base field F. The significance of being a Galois extension is that the extension has a Galois group and obeys...
8 KB (1,100 words) - 22:29, 3 May 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
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
In mathematics, differential Galois theory studies the Galois groups of differential equations. Whereas algebraic Galois theory studies extensions of...
3 KB (327 words) - 16:11, 28 April 2023