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Field theory (classical foundations and multiplicative groups)

Field theory (classical foundations and multiplicative groups) Acta Applicandae M athematicae 23: (1991). 189 Book Reviews Gregory Karpilovsky: Field Theory (Classical Foundations and Multiplicative Groups), Marcel Dekker, Inc., New York, 1988. Ever since the appearance of the monumental work on algebraic number theory known as Hilbert's Zahlbericht (see Ref. [4]), field theory has been an important and frequent subject of book length treatments. One may even make a case for claiming that among the most satisfying and beautiful chapters in modern mathematics is the study of finite, normal separable extensions of the field of rational numbers, with its applications to the problem of the solvability by radicals of polynomial equations of degree five or higher, i.e., classical Galois theory. Every serious modern algebra text expounds Galois theory to some extent, and there really are very many excellent texts specializing in various parts of the vast subject of the theory of fields. A few that come to mind are given below, but the list could easily be much longer! So when a book such as the one by G. Karpilovsky comes along and is presented as an 'informative reference/text' (from the blurb circulated by the publisher), it invites comparison with other quite successful publications. At first glance, http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Field theory (classical foundations and multiplicative groups)

Acta Applicandae Mathematicae , Volume 23 (2) – May 4, 2004

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References (9)

Publisher
Springer Journals
Copyright
Copyright
Subject
Mathematics; Computational Mathematics and Numerical Analysis; Applications of Mathematics; Partial Differential Equations; Probability Theory and Stochastic Processes; Calculus of Variations and Optimal Control; Optimization
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/BF00048805
Publisher site
See Article on Publisher Site

Abstract

Acta Applicandae M athematicae 23: (1991). 189 Book Reviews Gregory Karpilovsky: Field Theory (Classical Foundations and Multiplicative Groups), Marcel Dekker, Inc., New York, 1988. Ever since the appearance of the monumental work on algebraic number theory known as Hilbert's Zahlbericht (see Ref. [4]), field theory has been an important and frequent subject of book length treatments. One may even make a case for claiming that among the most satisfying and beautiful chapters in modern mathematics is the study of finite, normal separable extensions of the field of rational numbers, with its applications to the problem of the solvability by radicals of polynomial equations of degree five or higher, i.e., classical Galois theory. Every serious modern algebra text expounds Galois theory to some extent, and there really are very many excellent texts specializing in various parts of the vast subject of the theory of fields. A few that come to mind are given below, but the list could easily be much longer! So when a book such as the one by G. Karpilovsky comes along and is presented as an 'informative reference/text' (from the blurb circulated by the publisher), it invites comparison with other quite successful publications. At first glance,

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: May 4, 2004

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