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...

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...

In mathematics, Galois theory, originally introduced by Évariste Galois, provides a connection between field theory and group theory. This connection...

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...

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...

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...

mathematics, differential Galois theory is the field that studies extensions of differential fields. Whereas algebraic Galois theory studies extensions...

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...

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...

finite group the Galois group of a Galois extension of the rational numbers? (more unsolved problems in mathematics) In Galois theory, the inverse Galois problem...