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

geometry. Galois group for more examples Fundamental theorem of Galois theory Differential Galois theory for a Galois theory of differential equations...

is referred to as differential Galois theory, by analogy with algebraic Galois theory. The basic theorem of differential Galois theory is due to Joseph...

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

result of their theory says very roughly that a linear differential equation can be solved by quadratures if and only if its differential Galois group is connected...

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...

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...

Galois module Galois representation Galois ring Galois theory Differential Galois theory Topological Galois theory Inverse Galois problem Galois (crater)...

Picard–Vessiot theory which was initiated by Émile Picard and Ernest Vessiot, and whose recent developments are called differential Galois theory. The impossibility...

derivation d forms a differential algebra, and is itself a significant object of study in areas such as differential Galois theory. If A is a K-algebra...

References Galois cohomology an application of homological algebra, it is the study of group cohomology of Galois modules. Galois theory named after...

hypergeometric equation. In differential Galois theory the case of algebraic solutions is that in which the differential Galois group G is finite (equivalently...

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

local-global principle for linear ordinary differential equations, related to differential Galois theory and in a loose sense analogous to the result...

in number theory Difference algebra Differential algebraic geometry Differential calculus over commutative algebras Differential Galois theory – Study of...

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...

commutative algebra, Galois theory of rings, algebraic geometry, algebraic groups, representations of groups and differential Galois theory. He has also published...

variety Theta function Grassmannian Flag manifold Weil restriction Differential Galois theory Prime ideal Valuation (algebra) Krull dimension Regular local...

was to the theory of differential equations. On the model of Galois theory and polynomial equations, the driving conception was of a theory capable of...

function Closed-form expression Differential Galois theory Elementary function arithmetic Liouville's theorem (differential algebra) Tarski's high school...

number theory Galois groups of infinite algebraic field extensions are equipped with the Krull topology, which plays a role in infinite Galois theory. A generalization...

Galois group is p mod m. From this point of view, the distribution of Frobenius conjugacy classes in Galois groups over Q (or, more generally, Galois...

was to the theory of differential equations. On the model of Galois theory and polynomial equations, the driving conception was of a theory capable of...

algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical...

the same as cohomology theories?". MathOverflow. Switzer 1975, 7.68. Dieudonné, Jean (1989), History of Algebraic and Differential Topology, Birkhäuser...

branches of mathematics: topological Galois theory (with his student Askold Khovanskii), symplectic topology and KAM theory. Arnold was also a populariser of...

x^{x}\,\mathrm {d} x.} For a more detailed discussion, see also Differential Galois theory. Finding antiderivatives of elementary functions is often considerably...

set of operations Differential Galois theory – Study of Galois symmetry groups of differential fields Liouville's theorem (differential algebra) – Says...

continuous (differential equations), in particular the notions of integrability (Morales-Ramis theory) and the Galois differential theory. In 1982, Ramis...

group theory, Galois theory, control theory, and K-theory.) In particular there is no connotation of hypothetical. Thus the term unifying theory is more...