Galois theory. (2nd ed)

The book discusses classical Galois theory in considerable generality, treating fields of characteristic zero and of positive characteristic with consideration of both separable and inseparable extensions, but with a particular emphasis on algebraic extensions of the field of rational numbers. While...

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Main Author: Weintraub, Steven H.
Format: Book
Language:English
Published: Springer 2017
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Online Access:http://repository.vnu.edu.vn/handle/VNU_123/30866
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Institution: Vietnam National University, Hanoi
Language: English
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spelling oai:112.137.131.14:VNU_123-308662020-06-21T03:08:55Z Galois theory. (2nd ed) Weintraub, Steven H. Mathematics Statistics ; Galois theory -- Textbooks. 512.32 The book discusses classical Galois theory in considerable generality, treating fields of characteristic zero and of positive characteristic with consideration of both separable and inseparable extensions, but with a particular emphasis on algebraic extensions of the field of rational numbers. While most of the book is concerned with finite extensions, it discusses algebraic closure and infinite Galois extensions, and concludes with a new chapter on transcendental extensions (...) This is a textbook on Galois theory. Galois theory has a well-deserved re- tation as one of the most beautiful subjects in mathematics. I was seduced by its beauty into writing this book. I hope you will be seduced by its beauty in reading it. This book begins at the beginning. Indeed (and perhaps a little unusually for a mathematics text), it begins with an informal introductory chapter, Ch- ter 1. In this chapter we give a number of examples in Galois theory, even before our terms have been properly de?ned. (Needless to say, even though we proceed informally here, everything we say is absolutely correct.) These examples are sort of an airport beacon, shining a clear light at our destination as we navigate a course through the mathematical skies to get there. Then we start with our proper development of the subject, in Chapter 2. We assume no prior knowledge of ?eld theory on the part of the reader. We develop ?eld theory, with our goal being the Fundamental Theorem of Galois Theory (the FTGT). On the way, we consider extension ?elds, and deal with the notions of normal, separable, and Galois extensions. Then, in the penul- mate section of this chapter, we reach our main goal, the FTGT. 2017-04-19T02:17:49Z 2017-04-19T02:17:49Z 2009 Book 978-0-387-87574-3 http://repository.vnu.edu.vn/handle/VNU_123/30866 en 220 p. application/pdf Springer
institution Vietnam National University, Hanoi
building VNU Library & Information Center
country Vietnam
collection VNU Digital Repository
language English
topic Mathematics
Statistics ; Galois theory -- Textbooks.
512.32
spellingShingle Mathematics
Statistics ; Galois theory -- Textbooks.
512.32
Weintraub, Steven H.
Galois theory. (2nd ed)
description The book discusses classical Galois theory in considerable generality, treating fields of characteristic zero and of positive characteristic with consideration of both separable and inseparable extensions, but with a particular emphasis on algebraic extensions of the field of rational numbers. While most of the book is concerned with finite extensions, it discusses algebraic closure and infinite Galois extensions, and concludes with a new chapter on transcendental extensions (...)
format Book
author Weintraub, Steven H.
author_facet Weintraub, Steven H.
author_sort Weintraub, Steven H.
title Galois theory. (2nd ed)
title_short Galois theory. (2nd ed)
title_full Galois theory. (2nd ed)
title_fullStr Galois theory. (2nd ed)
title_full_unstemmed Galois theory. (2nd ed)
title_sort galois theory. (2nd ed)
publisher Springer
publishDate 2017
url http://repository.vnu.edu.vn/handle/VNU_123/30866
_version_ 1680963401524707328