Galois theory

The branch of mathematics dealing with Galois groups, Galois fields, and polynomial equations.

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  • Galois theory — [gal wä′] n. [after E. Galois (1811 32), Fr mathematician] a branch of algebra that determines if an algebraic equation can be solved in terms of radicals …   English World dictionary

  • Galois theory — In mathematics, more specifically in abstract algebra, Galois theory, named after Évariste Galois, provides a connection between field theory and group theory. Using Galois theory, certain problems in field theory can be reduced to group theory,… …   Wikipedia

  • Galois theory — noun Etymology: Évariste Galois Date: 1893 a part of the theory of mathematical groups concerned especially with the conditions under which a solution to a polynomial equation with coefficients in a given mathematical field can be obtained in the …   New Collegiate Dictionary

  • Galois theory — /gal wah /; Fr. /gann lwann /, Math. the branch of mathematics that deals with the application of the theory of finite groups to the solution of algebraic equations. [1890 95; named after Évariste Galois (1811 32), French mathematician] * * * …   Universalium

  • Galois theory — noun group theory applied to the solution of algebraic equations • Topics: ↑mathematics, ↑math, ↑maths • Hypernyms: ↑group theory …   Useful english dictionary

  • Differential Galois theory — In mathematics, differential Galois theory studies the Galois groups of differential equations. Whereas algebraic Galois theory studies extensions of algebraic fields, differential Galois theory studies extensions of differential fields, i.e.… …   Wikipedia

  • Grothendieck's Galois theory — In mathematics, Grothendieck s Galois theory is a highly abstract approach to the Galois theory of fields, developed around 1960 to provide a way to study the fundamental group of algebraic topology in the setting of algebraic geometry. It… …   Wikipedia

  • Fundamental theorem of Galois theory — In mathematics, the fundamental theorem of Galois theory is a result that describes the structure of certain types of field extensions.In its most basic form, the theorem asserts that given a field extension E / F which is finite and Galois,… …   Wikipedia

  • Galois-Theorie —   [ga lwa ], Algebra: von É. Galois entwickelte Theorie über den Zusammenhang zwischen den galoisschen Körpererweiterungen und ihren Galois Gruppen. Mithilfe der Galois Theorie lässt sich feststellen, ob eine algebraische Gleichung durch Radikale …   Universal-Lexikon

  • Galois connection — In mathematics, especially in order theory, a Galois connection is a particular correspondence between two partially ordered sets (posets). Galois connections generalize the correspondence between subgroups and subfields investigated in Galois… …   Wikipedia

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