Galois theory

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Ga·lois theory

The part of algebra concerned with the relation between solutions of a polynomial equation and the fields containing those solutions. It gives conditions under which the solutions can be expressed in terms of addition, subtraction, multiplication, division, and of the extraction of roots.

[After Évariste Galois (1811-1832), French mathematician.]
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

Galois theory

(Mathematics) maths the theory applying group theory to solving algebraic equations
[C19: named after Évariste Galois (1811–32), French mathematician]
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014
ThesaurusAntonymsRelated WordsSynonymsLegend:
Noun1.Galois theory - group theory applied to the solution of algebraic equations
math, mathematics, maths - a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement
group theory - the branch of mathematics dealing with groups
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To prove Proposition 1.1, we use the hypertranscendence criteria, established in the differential Galois theory. We will briefly recall this criteria and then, with the aid of it, prove Proposition 1.1.
Galois Theory and Applications: Solved Exercises and Problems
The necessary facts and results about differential Galois theory and its relations with the integrability of Hamiltonian systems, enough for our purposes, are written succinctly in Section 2 in [15] and we do not repeat them here.
The attempt to extend the Galois theory for commutative algebras, due to Chase, Harrison and Rosenberg [29], to the case of partial group actions (see reference [36]) spawned a new and unexpected development, namely the extension of the notion of partial actions to the realm of Hopf algebras.
Chapter nine returns to mathematics and logic as "the language of reason." Galois theory treats why certain math problems cannot be solved.
Moisil, and a few others, there were some isolated attempts of renewal, of incorporating, in university courses some achievements of mathematics in the 19th century and at the beginning of 20th century, such as the epsilon-delta analysis, crystallized by Cauchy, Riemann and Weierstrass, the Galois theory, the Cantor set theory, the theory of integral equations, modern logic, etc.
His textbook for graduate and undergraduate courses in number and Galois theory covers from Fermat to Gauss, class field theory, complex multiplication, and additional topics.
Chapters address group theory, commutative rings, Galois theory, noncommutative rings, representation theory, advanced linear algebra, and homology.
It seems possible that the Argand image may point the way to a more surveyable (or visualisable) form of a very abstract theory: the Galois Theory (see, for example, Littlewood, 1965, p.
And in the chapters on Bichat (chapter 4), Davy (chapter 5), and Galois (chapter 6) that follow, Chai traces out analogous distinctions between degrees of reflexivity, ranging from Bichat's attempt to develop a new theory of vitality, to Galois' more ambitious field theory; Galois theory could be extended to include new members in a group that are not yet known--a group defined by a "principle of containment" rather than an account of its elements (147).
One of the nicest actual constructions of the 17-gon is Richmond's (1893), as reproduced in Stewart's Galois Theory. Draw a circle centred at O, and choose one vertex V on the circle.