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

via Galois groups is called Galois theory, so named in honor of Évariste Galois who first discovered them. For a more elementary discussion of Galois groups...

His work laid the foundations for Galois theory and group theory, two major branches of abstract algebra. Galois was a staunch republican and was heavily...

Galois theory is parallel to algebraic Galois theory. One difference between the two constructions is that the Galois groups in differential Galois theory...

Galois theory is a result that describes the structure of certain types of field extensions in relation to groups. It was proved by Évariste Galois in...

especially in order theory, a Galois connection is a particular correspondence (typically) between two partially ordered sets (posets). Galois connections find...

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...

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 Artin...

the Galois groups of global fields are not known. Inverse Galois theory studies the (unsolved) problem whether any finite group is the Galois group...

Évariste Galois coined the term "group" and established a connection, now known as Galois theory, between the nascent theory of groups and field theory. In...

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...

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...

In mathematics, topological Galois theory is a mathematical theory which originated from a topological proof of Abel's impossibility theorem found by Vladimir...

mathematics, Galois cohomology is the study of the group cohomology of Galois modules, that is, the application of homological algebra to modules for Galois groups...

based on Galois theory comprise four main steps: the characterization of solvable equations in terms of field theory; the use of the Galois correspondence...

problem of Galois theory Given a group G, find an extension of the rational number or other field with G as Galois group. Differential Galois theory The subject...

speaking, a rational root if and only if the Galois group of p is included in G. More exactly, if the Galois group is included in G, then the resolvent...

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

F_{\infty }.} More generally, Iwasawa theory asks questions about the structure of Galois modules over extensions with Galois group a p-adic Lie group. Let p...

among themselves. The significance of the Galois group derives from the fundamental theorem of Galois theory, which proves that the fields lying between...

differential Galois theory, but this is not strictly true. The theorem can be proved without any use of Galois theory. Furthermore, the Galois group of a...

findings, the French mathematician Évariste Galois developed what came later to be known as Galois theory, which offered a more in-depth analysis of the...

In mathematics, the interplay between the Galois group G of a Galois extension L of a number field K, and the way the prime ideals P of the ring of integers...

by introducing what is now called Galois theory. Before Galois, there was no clear distinction between the "theory of equations" and "algebra". Since...

provides some information on the Galois group of P. More precisely, if R is separable and has a rational root then the Galois group of P is contained in G...

theory — Galois theory — Game theory — Gauge theory — Graph theory — Group theory — Hodge theory — Homology theory — Homotopy theory — Ideal theory —...

intermediate fields and the subgroups of the Galois group, described by the fundamental theorem of Galois theory. Field extensions can be generalized to ring...

In mathematics, p-adic Hodge theory is a theory that provides a way to classify and study p-adic Galois representations of characteristic 0 local fields...

higher do not have general solutions using radicals. Galois theory, named after Évariste Galois, showed that some equations of at least degree 5 do not...

Distribution theory Dynamical systems theory Elimination theory Ergodic theory Extremal graph theory Field theory Galois theory Game theory Graph theory Group...