The Theory Of Algebraic Number Fields
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The Theory of Algebraic Number Fields
Author | : David Hilbert |
Publsiher | : Springer Science & Business Media |
Total Pages | : 360 |
Release | : 2013-03-14 |
Genre | : Mathematics |
ISBN | : 9783662035450 |
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A translation of Hilberts "Theorie der algebraischen Zahlkörper" best known as the "Zahlbericht", first published in 1897, in which he provides an elegantly integrated overview of the development of algebraic number theory up to the end of the nineteenth century. The Zahlbericht also provided a firm foundation for further research in the theory, and can be seen as the starting point for all twentieth century investigations into the subject, as well as reciprocity laws and class field theory. This English edition further contains an introduction by F. Lemmermeyer and N. Schappacher.
Algebraic Number Fields
Author | : Gerald J. Janusz |
Publsiher | : American Mathematical Soc. |
Total Pages | : 288 |
Release | : 1996 |
Genre | : Algebraic fields |
ISBN | : 9780821804292 |
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This text presents the basic information about finite dimensional extension fields of the rational numbers, algebraic number fields, and the rings of algebraic integers in them. The important theorems regarding the units of the ring of integers and the class group are proved and illustrated with many examples given in detail. The completion of an algebraic number field at a valuation is discussed in detail and then used to provide economical proofs of global results. The book contains many concrete examples illustrating the computation of class groups, class numbers, and Hilbert class fields. Exercises are provided to indicate applications of the general theory.
The Theory of Algebraic Numbers Second Edition
Author | : Harry Pollard,Harold G. Diamond |
Publsiher | : American Mathematical Soc. |
Total Pages | : 162 |
Release | : 1975-12-31 |
Genre | : Algebraic number theory |
ISBN | : 9781614440093 |
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This monograph makes available, in English, the elementary parts of classical algebraic number theory. This second edition follows closely the plan and style of the first edition. The principal changes are the correction of misprints, the expansion or simplification of some arguments, and the omission of the final chapter on units in order to make way for the introduction of some two hundred problems.
The Genus Fields of Algebraic Number Fields
Author | : M. Ishida |
Publsiher | : Springer |
Total Pages | : 123 |
Release | : 2006-12-08 |
Genre | : Mathematics |
ISBN | : 9783540375531 |
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A Brief Guide to Algebraic Number Theory
Author | : H. P. F. Swinnerton-Dyer |
Publsiher | : Cambridge University Press |
Total Pages | : 164 |
Release | : 2001-02-22 |
Genre | : Mathematics |
ISBN | : 0521004233 |
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Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.
Number Fields
Author | : Daniel A. Marcus |
Publsiher | : Springer |
Total Pages | : 203 |
Release | : 2018-07-05 |
Genre | : Mathematics |
ISBN | : 9783319902333 |
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Requiring no more than a basic knowledge of abstract algebra, this text presents the mathematics of number fields in a straightforward, pedestrian manner. It therefore avoids local methods and presents proofs in a way that highlights the important parts of the arguments. Readers are assumed to be able to fill in the details, which in many places are left as exercises.
Classical Theory of Algebraic Numbers
Author | : Paulo Ribenboim |
Publsiher | : Springer Science & Business Media |
Total Pages | : 676 |
Release | : 2013-11-11 |
Genre | : Mathematics |
ISBN | : 9780387216904 |
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The exposition of the classical theory of algebraic numbers is clear and thorough, and there is a large number of exercises as well as worked out numerical examples. A careful study of this book will provide a solid background to the learning of more recent topics.
Elementary and Analytic Theory of Algebraic Numbers
Author | : Wladyslaw Narkiewicz |
Publsiher | : Springer Science & Business Media |
Total Pages | : 712 |
Release | : 2013-06-29 |
Genre | : Mathematics |
ISBN | : 9783662070017 |
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This book details the classical part of the theory of algebraic number theory, excluding class-field theory and its consequences. Coverage includes: ideal theory in rings of algebraic integers, p-adic fields and their finite extensions, ideles and adeles, zeta-functions, distribution of prime ideals, Abelian fields, the class-number of quadratic fields, and factorization problems. The book also features exercises and a list of open problems.