Comments:

111 pages, 2008

Abstract:

A concise presentation of Galois theory and the algebraic structure of Galois extensions; this is mirrored in the subgroups of their Galois groups, which allows the application of group theoretic ideas to the study of fields. "This Galois Correspondence is a powerful idea which can be generalized to apply to such diverse topics as ring theory, algebraic number theory, algebraic geometry, differential equations and algebraic topology." http://www.maths.gla.ac.uk/~ajb/dvi-ps/Galois.pdf AMS MSC: 12F10 (Field theory and polynomials :: Field extensions :: Separable extensions, Galois theory) 11R32 (Number theory :: Algebraic number theory: global fields :: Galois theory) 11S20 (Number theory :: Algebraic number theory: local and $p$-adic fields :: Galois theory) 13B05 (Commutative rings and algebras :: Ring extensions and related topics :: Galois theory)

Rights:

Open; for student study http://www.maths.gla.ac.uk/~ajb/dvi-ps/Galois.pdf

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