The Genus Fields of Algebraic Number Fields
Author | : M. Ishida |
Publisher | : Springer |
Total Pages | : 123 |
Release | : 2006-12-08 |
Genre | : Mathematics |
ISBN | : 3540375538 |
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Author | : M. Ishida |
Publisher | : Springer |
Total Pages | : 123 |
Release | : 2006-12-08 |
Genre | : Mathematics |
ISBN | : 3540375538 |
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Author | : Makoto Ishida |
Publisher | : Springer |
Total Pages | : 115 |
Release | : 1976-01-01 |
Genre | : Algebraic fields |
ISBN | : 9780387080000 |
Author | : Gerald J. Janusz |
Publisher | : American Mathematical Soc. |
Total Pages | : 288 |
Release | : 1996 |
Genre | : Mathematics |
ISBN | : 0821804294 |
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.
Author | : Daniel A. Marcus |
Publisher | : Springer |
Total Pages | : 213 |
Release | : 2018-07-05 |
Genre | : Mathematics |
ISBN | : 3319902334 |
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.
Author | : Wladyslaw Narkiewicz |
Publisher | : Springer Science & Business Media |
Total Pages | : 712 |
Release | : 2013-06-29 |
Genre | : Mathematics |
ISBN | : 3662070014 |
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.
Author | : Andre Weil |
Publisher | : Springer Science & Business Media |
Total Pages | : 332 |
Release | : 2013-12-14 |
Genre | : Mathematics |
ISBN | : 3662059789 |
Itpzf}JlOV, li~oxov uoq>ZUJlCJ. 7:WV Al(JX., llpoj1. AE(Jj1. The first part of this volume is based on a course taught at Princeton University in 1961-62; at that time, an excellent set ofnotes was prepared by David Cantor, and it was originally my intention to make these notes available to the mathematical public with only quite minor changes. Then, among some old papers of mine, I accidentally came across a long-forgotten manuscript by ChevaIley, of pre-war vintage (forgotten, that is to say, both by me and by its author) which, to my taste at least, seemed to have aged very welt It contained abrief but essentially com plete account of the main features of c1assfield theory, both local and global; and it soon became obvious that the usefulness of the intended volume would be greatly enhanced if I inc1uded such a treatment of this topic. It had to be expanded, in accordance with my own plans, but its outline could be preserved without much change. In fact, I have adhered to it rather c10sely at some critical points.
Author | : Zhang Xian Ke |
Publisher | : ALPHA SCIENCE INTERNATIONAL LIMITED |
Total Pages | : 417 |
Release | : 2016-03-14 |
Genre | : Mathematics |
ISBN | : 1783323094 |
ALGEBRAIC NUMBER THEORY provides concisely both the fundamental and profound theory, starting from the succinct ideal theory (Chapters 1-3), turning then to valuation theory and local completion field (Chapters 4-5) which is the base of modern approach. After specific discussions on class numbers, units, quadratic and cyclotomic fields, and analytical theory (Chapters 6-8), the important Class Field Theory (Chapter 9) is expounded, and algebraic function field (Chapter 10) is sketched. This book is based on the study and lectures of the author at several universities.
Author | : |
Publisher | : Academic Press |
Total Pages | : 233 |
Release | : 1973-08-15 |
Genre | : Mathematics |
ISBN | : 0080873707 |
Algebraic Number Fields
Author | : David Hilbert |
Publisher | : Springer Science & Business Media |
Total Pages | : 360 |
Release | : 2013-03-14 |
Genre | : Mathematics |
ISBN | : 3662035456 |
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.
Author | : J. W. P. Hirschfeld |
Publisher | : Princeton University Press |
Total Pages | : 717 |
Release | : 2013-03-25 |
Genre | : Mathematics |
ISBN | : 1400847419 |
This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental importance to mathematics for many years and that has essential applications in areas such as finite geometry, number theory, error-correcting codes, and cryptology. Unlike other books, this one emphasizes the algebraic geometry rather than the function field approach to algebraic curves. The authors begin by developing the general theory of curves over any field, highlighting peculiarities occurring for positive characteristic and requiring of the reader only basic knowledge of algebra and geometry. The special properties that a curve over a finite field can have are then discussed. The geometrical theory of linear series is used to find estimates for the number of rational points on a curve, following the theory of Stöhr and Voloch. The approach of Hasse and Weil via zeta functions is explained, and then attention turns to more advanced results: a state-of-the-art introduction to maximal curves over finite fields is provided; a comprehensive account is given of the automorphism group of a curve; and some applications to coding theory and finite geometry are described. The book includes many examples and exercises. It is an indispensable resource for researchers and the ideal textbook for graduate students.