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＜電子ブック＞
Fields and Galois Theory / by John M. Howie
(Springer Undergraduate Mathematics Series. ISSN:21974144)

版	1st ed. 2006.
出版者	(London : Springer London : Imprint: Springer)
出版年	2006
本文言語	英語
大きさ	X, 226 p. 22 illus : online resource
著者標目	*Howie, John M author SpringerLink (Online service)
件　名	LCSH:Algebra LCSH:Algebraic fields LCSH:Polynomials FREE:Algebra FREE:Field Theory and Polynomials
一般注記	Rings and Fields -- Integral Domains and Polynomials -- Field Extensions -- Applications to Geometry -- Splitting Fields -- Finite Fields -- The Galois Group -- Equations and Groups -- Some Group Theory -- Groups and Equations -- Regular Polygons -- Solutions The pioneering work of Abel and Galois in the early nineteenth century demonstrated that the long-standing quest for a solution of quintic equations by radicals was fruitless: no formula can be found. The techniques they used were, in the end, more important than the resolution of a somewhat esoteric problem, for they were the genesis of modern abstract algebra. This book provides a gentle introduction to Galois theory suitable for third- and fourth-year undergraduates and beginning graduates. The approach is unashamedly unhistorical: it uses the language and techniques of abstract algebra to express complex arguments in contemporary terms. Thus the insolubility of the quintic by radicals is linked to the fact that the alternating group of degree 5 is simple - which is assuredly not the way Galois would have expressed the connection. Topics covered include: rings and fields integral domains and polynomials field extensions and splitting fields applications to geometry finite fields the Galois group equations Group theory features in many of the arguments, and is fully explained in the text. Clear and careful explanations are backed up with worked examples and more than 100 exercises, for which full solutions are provided HTTP:URL=https://doi.org/10.1007/978-1-84628-181-5

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