# Galois theory

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## Ga·lois theory

(găl-wä′)
n.
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.]

## Galois theory

(ˈɡælwɑː)
n
(Mathematics) maths the theory applying group theory to solving algebraic equations
[C19: named after Évariste Galois (1811–32), French mathematician]
ThesaurusAntonymsRelated WordsSynonymsLegend:
 Noun 1 Galois theory - group theory applied to the solution of algebraic equationsmath, mathematics, maths - a science (or group of related sciences) dealing with the logic of quantity and shape and arrangementgroup theory - the branch of mathematics dealing with groups
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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.
Several problems in effective Galois theory (see [Girstmair(1987), Abdeljaouad(2000)]), computational commutative algebra (see [Faugere and Rahmany(2009), Borie and Thiery(2011), Borie(2011)]) and generation of unlabeled with repetitions species of structures rely on the following computational building block.
Other revisions to this second edition include an earlier introduction to noncommutative rings; a simpler treatment of the existence of free groups; and new discussions of Galois theory for infinite extensions, the normal basis theory, abelian categories, and module categories.
One of the nicest actual constructions of the 17-gon is Richmond's (1893), as reproduced in Stewart's Galois Theory.
The modern approach to Galois theory is undeniably elegant, says Newman (emeritus psychiatry, U.
This mathematics textbook for graduate students covers the fundamentals of abstract algebra including fields and Galois theory, algebraic number theory, algebraic geometry and groups, rings and modules.
With a focus on prominent areas such as the numerical solutions of equations, the systematic study of equations, and Galois theory, this book facilitates a thorough understanding of algebra and illustrates how the concepts of modern algebra originally developed from classical algebraic precursors.

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