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M. Eichler (1966)
Introduction to the Theory of Algebraic Numbers and Functions
P. McCarthy (1966)
Algebraic extensions of fields
W. Ledermann (1966)
Lectures in Abstract Algebra : vol. III, Theory of Fields and Galois Theory. By N. Jacobson. Pp. xi, 323. 76s. (Van Nostrand)The Mathematical Gazette, 50
Z. I. Borevich, I. R. Shafarevich (1966)
Number Theory
Kennan Smith (1987)
Power series from a computational point of view
S. Lang (1971)
Algebraic Number Theory
D. Hilbert (1932)
Hilbert's Gesammelte Abhandlungen
S. Lang (1989)
Cyclotomic Fields I and II
D. Hilbert (1932)
Die Theorie der algebraischen ZahlkörperJahresbericht Der Deutschen Mathematiker-vereinigung, 4
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,
Acta Applicandae Mathematicae – Springer Journals
Published: May 4, 2004
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