The Genus Fields of Algebraic Number Fields
| Author | : M. Ishida |
| Publisher | : Springer |
| Total Pages | : 123 |
| Release | : 2006-12-08 |
| Genre | : Mathematics |
| ISBN | : 3540375538 |
a
The Genus Fields Of Algebraic Number Fields
Download The Genus Fields Of Algebraic Number Fields full books in PDF, epub, and Kindle. Read online free The Genus Fields Of Algebraic Number Fields ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
The Genus Fields of Algebraic Number Fields
| Author | : Makoto Ishida |
| Publisher | : Springer |
| Total Pages | : 115 |
| Release | : 1976-01-01 |
| Genre | : Algebraic fields |
| ISBN | : 9780387080000 |
Algebraic Number Fields
| 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.
Number Fields
| 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.
A Classical Invitation to Algebraic Numbers and Class Fields
| Author | : Harvey Cohn |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 344 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461299500 |
"Artin's 1932 Göttingen Lectures on Class Field Theory" and "Connections between Algebrac Number Theory and Integral Matrices"
Elementary and Analytic Theory of Algebraic Numbers
| 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.
Algebraic Number Theory
| 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.
Algebraic Number Fields
| Author | : |
| Publisher | : Academic Press |
| Total Pages | : 233 |
| Release | : 1973-08-15 |
| Genre | : Mathematics |
| ISBN | : 0080873707 |
Algebraic Number Fields
The Theory of 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.
Introduction to Cyclotomic Fields
| Author | : Lawrence C. Washington |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 504 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461219345 |
This text on a central area of number theory covers p-adic L-functions, class numbers, cyclotomic units, Fermat’s Last Theorem, and Iwasawa’s theory of Z_p-extensions. This edition contains a new chapter on the work of Thaine, Kolyvagin, and Rubin, including a proof of the Main Conjecture, as well as a chapter on other recent developments, such as primality testing via Jacobi sums and Sinnott’s proof of the vanishing of Iwasawa’s f-invariant.
